Proctored - Mock CAT – 7
Test Booklet Serial Number: 7 7 0 9 5 0
INSTRUCTIONS
1.
This Test contains 18 pages and 60 questions.
2.
This test has three sections that examine various abilities.
Section-I has 25 questions, Section-II has 20 questions and Section-III has 15 questions
You will be given 135 minutes to complete the test.
In distributing the time over the sections, please bear in mind that you need to demonstrate your
competence in all three sections.
3.
All questions carry 3 marks each. Each wrong answer will attract a penalty of 1 mark.
MBA
Test Prep
SECTION – I
VERBAL ABILITY
DIRECTIONS for Questions 1 to 4: The passage given below is followed by a set of questions. Choose the
best answer to each question.
PASSAGE - I
“LIKE elaborately plumed birds…we preen and strut and display our t-values.” That was Edward Leamer’s
uncharitable description of his profession in 1983. Mr Leamer, an economist at the University of California in
Los Angeles, was frustrated by empirical economists’ emphasis on measures of correlation over underlying
questions of cause and effect, such as whether people who spend more years in school go on to earn more in
later life. Hardly anyone, he wrote gloomily, “takes anyone else’s data analyses seriously”. To make his
point, Mr Leamer showed how different (but apparently reasonable) choices about which variables to include
in an analysis of the effect of capital punishment on murder rates could lead to the conclusion that the death
penalty led to more murders, fewer murders, or had no effect at all.
In the years since, economists have focused much more explicitly on improving the analysis of cause and
effect, giving rise to what Guido Imbens of Harvard University calls “the causal literature”. The techniques at
the heart of this literature—in particular, the use of so-called “instrumental variables”—have yielded insights
into everything from the link between abortion and crime to the economic return from education. But these
methods are themselves now coming under attack.
Instrumental variables have become popular in part because they allow economists to deal with one of the
main obstacles to the accurate estimation of causal effects—the impossibility of controlling for every last
influence. Mr Leamer’s work on capital punishment demonstrated that the choice of controls matters hugely.
Putting too many variables into a model ends up degrading the results. Worst of all, some relevant variables
may simply not be observable. For example, the time someone stays in school is probably influenced by his
innate scholastic ability, but this is very hard to measure. Leaving such variables out can easily lead
econometricians astray. What is more, the direction of causation is not always clear. Working out whether
deploying more policemen reduces crime, for example, is confused by the fact that more policemen are
allocated to areas with higher crime rates.
Instrumental variables are helpful in all these situations. Often derived from a quirk in the environment or in
public policy, they affect the outcome only through their influence on the input variable while at the same
time being uncorrelated with what is left out . The job of instrumental variables is to ensure that the omission
of factors from an analysis—does not end up producing inaccurate results.
In an influential early example of this sort of study, Joshua Angrist of the Massachusetts Institute of Technology (MIT) and Alan Krueger of Princeton University used America’s education laws to create an instrumental
variable based on years of schooling. These laws mean that children born earlier in the year are older when
they start school than those born later in the year, which means they have received less schooling by the time
they reach the legal leaving-age. Since a child’s birth date is unrelated to intrinsic ability, it is a good instrument for teasing out schooling’s true effect on wages. Over time, uses of such instrumental variables have
become a standard part of economists’ set of tools. Freakonomics, the 2005 bestseller by Steven Levitt and
Stephen Dubner, provides a popular treatment of many of the techniques. Mr Levitt’s analysis of crime during
American election cycles, when police numbers rise for reasons unconnected to crime rates, is a celebrated
example of an instrumental variable.
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Test Prep
Proctored - Mock CAT 7
1.
What does Edward Leamer imply by the comment in the first line of the passage?
(a) Birds are hollow creatures who do not care about their fellow birds.
(b) Every economist tries his best to promote his work.
(c) The economists who markets his ideas the most wins in the end like a well plumed bird.
(d) Economists are conceited creatures who display a behaviour similar to plumed birds in the sense
that they put down other economists for promoting themselves.
2.
In the schooling example talked about in various parts of the passage , which of the following options
correctly represents ‘the input variable’, ‘the outcome’ and ‘the left-out variable’ in order, from left to
right ?
(a) Scholastic ability, Earnings, Time spent in school.
(b) Earnings, Scholastic ability, Time spent in school.
(c) Time spent in school, Earnings, Scholastic ability.
(d) Time spent in school, Scholastic ability, Earnings.
3.
Which of the following would be a suitable title for the passage ?
(a) The role of instrumental variables in “causal literature.”
(b) Why the “causal literature” has become popular in economics.
(c) Instrumental variables and their influence on economics.
(d) Instrumental variables- the answer to unobservable factors.
4.
Which of the following can be inferred from the passage ?
(a) The techniques of “causal literature” have helped economists to overcome many an obstacle and
have received a unanimous acceptance from all.
(b) Instrumental variables affect the input variable as well as the uncorrelated factors which are left out.
(c) The instrumental variable created by Joshua and Alan makes it reasonably clear that the years of
schooling do not affect the wages earned after schooling.
(d) None of the above.
DIRECTION for question 5: There are two blanks in the following sentence. From the pair of words given,
choose the one that fills the blanks most appropriately. The first word in the pair should fill the first blank.
5.
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The present time seems ___________ to bad ideas. In the process of throwing off the shackles of
tradition, we have ended up being quite __________ incipient theories and untested solutions.
(a) hospitable....vulnerable to
(b) hostile....tolerant of
(c) prone....wary of
(d) impervious....exposed to
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Proctored - Mock CAT 7
DIRECTION for Question 6: This question presents a sentence, part of which or all of which is underlined.
Beneath the sentence you will find four ways of phrasing the underlined part. The first of these repeats the
original; the other three are different. If you think the original is best, choose the first answer; otherwise
choose one of the others. This question tests correctness and effectiveness of expression. In choosing your
answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of
words, and sentence construction. Choose the answer that produces the most effective sentence; this answer
should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.
6.
Companies, which use sophisticated machinery and produce high quality products, understand the
needs of their customers.
(a) Companies, which use sophisticated machinery and produce high quality products, understand the
needs
(b) Companies that use sophisticated machinery and produce high quality products understands the
needs
(c) Companies using sophisticated machinery and produce high quality products understand the needs
(d) Companies that use sophisticated machinery and produce high quality products understand the
needs
DIRECTION for Question 7: In the question, there are five sentences. Each sentence has a pair of words that
are italicised and highlighted. From the italicised and highlighted words, select the most appropriate words
(A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may
be selected to correctly complete the set of sentences. From the options given, choose the most appropriate
one.
7.
She refused to be phased (A) / fazed (B) by their insulting remarks. The palace was bombarded with
canon (A) / cannon (B) fires by the enemy. According to the law, all citizens must be given equitable
(A) / equable (B) treatment. As soon as the king died, lawlessness reigned (A) / reined (B) over the city.
Such inflammable (A) / inflammatory (B) remarks could lead to a communal discord.
(a) BBAAB
(b) ABAAB
(c) BBBAB
(d) BAAAA
DIRECTION for question 8: There are two blanks in the following sentence. From the pair of words given,
choose the one that fills the blanks most appropriately. The first word in the pair should fill the first blank.
8.
Page
In the next few years, the sophisticated satellites orbiting the Earth will generate enough data to determine whether the continents are moving at all or not, ______________ the inchoate ____________
among geographers about the truthfulness of the theory of continental drift.
(a) portending....rumors
(b) forestalling....rift
(c) settling....disturbances
(d) resolving....schism
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DIRECTION for Question 9: The following question has a paragraph from which the last sentence that
completes the paragraph has been deleted. From the given options, choose the sentence that completes the
paragraph in the most appropriate way.
9.
The question is whether the mind can function as its own cause, without having first experienced a
determining impulse. Not the activity of the mind but only the nature and the origin of this activity are
subject to question. In order to understand this clearly, we start out from the assumption that the mind
is one of the tools of the animal organism in the struggle for existence. From the beginnings of its
functioning in the simplest animals in which it first appears, the mind encounters two factors: on the one
hand, the body of the organism, which produces the mental functions, a body with certain innate needs
and capacities. Let us call it the “ego.” On the other hand, there is its environment: the “non-ego,”
which is the negation of the organism. ______________________________________.
(a) The more it understands its own needs and capacities as well as the differences and relationships
among the objects in the environment, the better it solves them.
(b) It is this awareness of the environment that contains the seed of its own negation, which is particularly striking.
(c) It is this environment that poses the perplexing problems the mind has to solve.
(d) It is the resolution of the antagonism between ego and environment that triggers adaptation.
DIRECTIONS for Questions 10 to 12:
12:The passage given below is followed by a set of questions. Choose
the best answer to each question.
PASSAGE - II
George Orwell wrote Animal Farm, “. . . to discredit the Soviet system by showing its inhumanity and its
back-sliding from ideals [he] valued . . .” Orwell noted that “ there exists in England almost no literature of
disillusionment with the Soviet Union.’ Instead, that country is viewed either with ignorant disapproval’ or
with uncritical admiration.’” The basic synopsis is this: Old Major, an old boar in Manor Farm, tells the other
animals of his dream of “animalism”: “ . . . Only get rid of Man, and the produce of our labour would be our
own. Almost overnight we would become rich and free.’” The other animals take this utopian idea to heart,
and one day actually do revolt and drive the humans out.
Two pigs emerge as leaders: Napoleon and Snowball. They constantly argued, but one day, due to a difference over plans to build a windmill, Napoleon exiled Snowball. Almost immediately, Napoleon established a
totalitarian government. Soon, the pigs began to get special favours, until finally, they were indistinguishable
from humans to the other animals. Immediately the reader can begin to draw parallels between the book’s
characters and the government in 1917-44 Russia. For example, Old Major, who invented the idea of “animalism,” is seen as representing Karl Marx, the creator of communism. Snowball represents Trotsky, a Russian leader after the revolution. He was driven out by Napoleon, who represents Stalin, the most powerful
figure in the country. Napoleon then proceeded to remove the freedoms of the animals, and established a
dictatorship, under the public veil of “animalism.” Pigs represent the ruling class because of their stereotype:
dirty animals with insatiable appetites. Boxer, the overworked, incredibly strong, dumb horse represents the
common worker in Russia. The two surrounding farms represent two of the countries on the global stage with
Russia at the time, Germany and England.
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Proctored - Mock CAT 7
Orwell begins his book by criticizing the capitalists and ruling elite, who are represented in Animal Farm by
Mr. Jones, the farmer. He is shown as a negligent drunk, who constantly starved his animals. “His character is
already established as self-indulgent and uncaring.” Orwell shows us how, “if only animals became aware of
their strength, we should have no power over them, and that men exploit animals in much the same way as the
rich exploit the proletariat.” What was established in Russia after the Bolshevik Revolution was not true
communism (“animalism”), which Orwell approved of, where the people owned all the factories and land.
Rather, “state communism” was established, where a central government owned them. Orwell thought that
such a political system, “state communism,” was open to exploitation by its leaders. Napoleon, after gaining
complete control, did anything he wished - reserved the best for the pigs, and treated the animals cruelly. The
animals could not do anything, unless they again realized their strength in numbers against their own kind.
Unfortunately, they were too stupid to realize this and accepted the “status quo.”
10.
All of the following would be in line with Orwell’s views except?
(a) Literature which expresses disillusionment about the Soviet Union is non-existent.
(b) The Soviet Union is viewed with extreme emotions by the British, who either disapprove of it
without knowledge or totally admire it.
(c) The rich are able to exploit the proletariat mainly because the proletariat is not aware of its own
strength.
(d) The capitalists are generally people who are involved in gratifying their self and have no empathy
towards others.
11.
Which of the following tones is not displayed by the author in the passage ?
(a) Objective
(b) Narrative
(c) Descriptive
(d) Critical
12.
According to the passage, the following four themes appear in the book ‘ The Animal Farm’. Select the
option which represents the correct sequence in which they occur in the book.
A. The revolting class acquiring a resemblance to the driven out class.
B. Establishment of a new ideology and exploiting the ideology.
C. The ruling elite exploiting those under them.
D. One leader driving out the other.
(a) ACBD
(b) CBDA
(c) CDBA
(d) BACD
DIRECTION for Question 13: The following question consists of two words that have a certain relationship
with each other followed by alternatives. Select the alternative that has the same relationship as depicted in the
original pair of words.
13.
Page
Secular: Mundane
(a) preposterous : prudent
(b) transient : fugacious
(c) recalcitrant : authoritative
(d) patent : closed
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Proctored - Mock CAT 7
DIRECTION for Question 14: Read the argument and answer the question that follows.
14.
The Government of India has imposed a heavy duty on petrol to discourage the consumption of the
same. The money accrued through the duty is used to subsidize the price charged for the fertilizers
distributed to poor farmers. So, greater the success achieved in meeting the first objective, the lesser
will be the success achieved in meeting the second objective.
The conclusion drawn above is most suitable in which of the following situations?
(a) A public library has imposed a heavy fine to force the borrowers to return the book promptly, when
due. The money accrued from the fines is used to send the reminders to those borrowers who did not
return books on time.
(b) A zoological garden has imposed an additional visitor’s tax over the normal entry fees to improve
facilities at the zoo. The money accrued will be used to improve the facilities for the upkeep of the
animals and to improve the recreational facilities at the zoo.
(c) The Delhi Metro Railway Corporation has imposed a user surcharge to prompt commuters to use
other means of transport. The money collected from the taxes will be used to expand the metro
services in other areas.
(d) The Government has imposed a heavy fine to dissuade people from littering in public places. The
money accrued from fines is used to pay overtime to the employees to clean the litter.
DIRECTION for Question 15: The following question has a paragraph from which the last sentence has
been deleted. From the given options, choose the sentence that completes the paragraph in the most appropriate way.
15.
Page
While the excellence and superlative quality of our traditional designs are undeniable, design cannot be
said to have a large role to play in our everyday lives today. Being conservative by nature, we do not
seem to care much for the aesthetics of contemporary design — too bleak and spare for our questionable tastes moulded largely by Bollywood and kitsch, and often bordering on the bizarre. When the rich
build houses, they prefer the excesses of neo-classical architecture to the luxury of ‘less is more.’
(a) Hence, our everyday lives are cluttered with cheap imitations and shallow designs.
(b) Thus, traditional designs will always find little or no acceptance in our everyday lives.
(c) For, the grand or what is perceived as grand is regarded as a symbol of power meant to impress and
perhaps even intimidate.
(d) Undoubtedly, popular designs are largely accepted no matter how bizarre they may really be.
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DIRECTION for Question 16: In the question, four different ways of presenting an idea are given. Choose
the one that conforms most closely to Standard English Usage.
16.
(a) Research is generally a tedious and frustrating process because there are just too much things that
are said about one particular subject and the researcher will be finding the ones relevant to his
research.
(b) The process of research is generally tedious and frustrating because there is just too many things
that are said about one particular subject and the researcher must be finding the ones relevant to his
research.
(c) The process of research is generally tedious and frustrating because there are just too many things
that are said about one particular subject and the researcher must find the ones relevant to his
research.
(d) Generally research is a tedious and frustrating process because there are just too many things that
are said about one particular subject and the researcher must find the ones relevant to his research.
DIRECTION for question 17: There are two blanks in the following sentence. From the pair of words given,
choose the one that fills the blanks most appropriately. The first word in the pair should fill the first blank.
17.
Most of the fifteenth and sixteenth century Mughal gardens were not necessarily intended to look
______________. These gardens were designed to conjure the profound melancholy ensuing from a
sense of the ______________ of natural beauty and human glory.
(a) blitheful....immutability
(b) beautiful....persistence
(c) blissful....simplicity
(d) cheerful....fleetingness
DIRECTION for Question 18: Read the argument and answer the question that follows.
18.
Professor: Students in the graduate courses do not write as well as they used to do in the past. Most of
the papers submitted to me by my students have been badly written. These papers also carry lot of
grammatical errors.
Which one of the following is the most serious weakness in the argument made by the professor?
(a) The professor is generalizing about all graduate students on the basis of the submissions of his
students.
(b) There is no proof that the professor is a competent judge of English language.
(c) The argument does not define the criterion for judging a good paper.
(d) The argument does not take into account that the professor is a bad teacher.
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DIRECTION for Question 19: The following question consists of two words that have a certain relationship
with each other followed by alternatives. Select the alternative that has the same relationship as depicted in the
original pair of words.
19.
Formation: Soldiers
(a) club : members
(b) array : numbers
(c) forest : trees
(d) matrix : columns
DIRECTION for Question 20: Fill in the blank of the following sentence using one from the idioms provided in the four alternatives.
20.
With a coastline of over 3,000km and a fishing fleet of more than 1,000 vessels, it’s ironic that Vietnam
has to import powdered fish from Peru. In a country with huge agricultural potential, this import is like
“_____________”.
(a) carrying coals to Newcastle
(b) to take a running jump
(c) raking over the coals
(d) a running battle
DIRECTION for Question 21: The following question has a paragraph from which the last sentence that
completes the paragraph has been deleted. From the given options, choose the sentence that completes the
paragraph in the most appropriate way.
21.
Page
How true it is that our children do not belong to us ! We try desperately to give them our thoughts, and
yet they have their own thoughts. As parents, we can house our children’s bodies, but not their souls.
When they reach an age of independence, they are finding their way, and they are torn between needing our help, and needing to be on their own. I remember that feeling clearly. There was such an
excitement about being alive, and I was sure that no one else knew the things that I knew, or felt the
things that I felt. I was learning that parents weren’t always right about everything, and some rules
seemed worth breaking. I guess we all go through at least a little rebellion.
_________________________________.
(a) And when this is realized there is also a brief maudlinness accompanied with frequent twinges of
self-abasement in our attitudes, which our parents can easily identify.
(b) And as our children’s souls live in the house of tomorrow-a place we cannot visit, not even in our
dreams, even mistakes are part of our journey.
(c) And as parents, we are the bow that sends the living arrows into the future, but it is the Archer (who
guides us) that directs the swiftness and the distance of the arrows, to His directed destination.
(d) And we certainly develop our own thoughts as it is a part of finding ourselves and our capabilities.
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DIRECTIONS for Questions 22 to 24: The passage given below is followed by a set of questions. Choose
the best answer to each question.
PASSAGE - III
Haffner, like Delboeuf, has attempted to explain the act of dreaming by the alteration which an abnormally
introduced condition must have upon the otherwise correct functioning of the intact psychic apparatus; but he
describes this condition in somewhat different terms. He states that the first distinguishing mark of dreams is
the abolition of time and space, i.e., the emancipation of the representation from the individual’s position in
the spatial and temporal order. Associated with this is the second fundamental character of dreams, the mistaking of the hallucinations, imaginations, and fantasy-combinations for objective perceptions. “The sumtotal of the higher psychic functions, particularly the formation of concepts, judgments, and conclusions on
the one hand, and free self-determination on the other hand, combine with the sensory fantasy-images, and at
all times have these as a substratum”. These activities too, therefore, participate in the erratic nature of the
dream-representations. We say they participate, for our faculties of judgment and will are in themselves
unaltered during sleep. As far as their activity is concerned, we are just as shrewd and just as free as in the
waking state.
A man cannot violate the laws of thought; that is, even in a dream he cannot judge things to be identical which
present themselves to him as opposites. He can desire in a dream only that which he regards as a good (sub
ratione boni). But in this application of the laws of thought and will the human intellect is led astray in dreams
by confusing one notion with another. Thus it happens that in dreams we formulate and commit the greatest
of contradictions, while, on the other hand, we display the shrewdest judgment and arrive at the most logical
conclusions, and are able to make the most virtuous and sacred resolutions. “The lack of orientation is the
whole secret of our flights of fantasy in dreams, and the lack of critical reflection and agreement with other
minds is the main source of the reckless extravagances of our judgments, hopes and wishes in dreams”
If the turning-away from the outer world is accepted as the decisive cause of the most conspicuous characteristics of our dreams, it will be worth our while to consider certain subtle observations of Burdach’s, which will
throw some light on the relation of the sleeping psyche to the outer world, and at the same time serve to
prevent our over-estimating the importance of the above deductions. “Sleep,” says Burdach, “results only
under the condition that the mind is not excited by sensory stimuli... yet it is not so much a lack of sensory
stimuli that conditions sleep as a lack of interest in them; some sensory impressions are even necessary in so
far as they serve to calm the mind; thus the miller can fall asleep only when he hears the clatter of his mill, and
he who finds it necessary, as a matter of precaution, to burn a light at night, cannot fall asleep in the dark”
22.
Which of the following can be inferred to be a cause of dreams ?
(a) The turning-away from the outer world.
(b) Excitation of the sleeping mind by sensory stimuli.
(c) Dissonance experienced with others.
(d) None of the above.
23.
The mistaking of the hallucinations in a dream for objective perceptions is associated with which of the
following?
A. Emancipation of representation from the individual’s position in the spatial and temporal order.
B. Our faculties of judgment and will being unaltered during sleep.
C. The fact that man can desire in a dream only that which he feels would be good for him.
(a) Only B
(b) A and B
(c) B and C
(d) A and C
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24.
The author develops the passage by
(a) Showing how Haffner’s explanation regarding dreams is different from that of Delboeuf and then
moving on to give more clarity on Haffner’s explanation.
(b) Throwing light on Haffner’s explanation as regards dreams and then attempting to moderate it.
(c) First discussing the explanations for dreams given by Haffner and then attempting to move on to
Burdach’s explanations for more clarity and moderation on the initial discussion.
(d) Discussing Haffner’s explanation for dreams and then moving on to Burdach’s observations for
moderation on the initial discussion after assuming one of the fundamental assumptions of Burdach
to be true.
DIRECTION for Question 25: Fill in the blank of the following sentence using one from the idioms provided
in the four alternatives.
25.
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Eat carrots for better eyesight, but also know that its excess consumption can turn your skin an orange
hue. Some ____________ are just silly superstitions, but some may just have a nugget of truth.
(a) old heave-hos
(b) open sesames
(c) old flames
(d) old wives’ tales
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SECTION – II
QUANTITATIVE ABILITY
26.
A sequence ‘S’ is formed from the set of first ‘N’ natural numbers by deleting all the perfect squares and
all the perfect cubes. If the elements are arranged in an ascending order then, what is the 240th term of
the sequence ‘S’?
(a) 259
(b) 260
(c) 261
(d) 262
27.
What is the remainder when 1366 – 23 is divided by 183?
(a) 0
(b) 161
(c) 22
(d) 162
28.
The sum of the coefficients of the polynomial (x – 1) (x – 2) (x – 4) is
(a) 0
(b) 16
(c) –16
(d) None of these
29.
Given that a, b, c, and d are positive integers such that b3/2 = a, and d5/4 = c. If b – d = 9, then find the
value of (a – c).
(a) 92
(b) 94
(c) 95
(d) 93
30.
Consider the set G of all integers between 100 and 9999 (including the extremes). Call two integers a
and b in G to be in the same category if the digits appearing in a and b are the same. For example, if
a = 101, b = 100, c = 1000 and d = 120, then a, b and c are in the same category but c and d are not. Find
the number of different categories that can be formed out of G.
(a) 384
(b) 385
(c) 174
(d) 175
31.
The numbers (7 – a), (7 – b), (7 – c), (7 – d) and (7 – e) are all distinct integers whose product is equal
to 28. What is the sum (a + b + c + d + e)?
(a) 13
(b) 7
(c) 28
(d) Data Inconsistent
32.
In a factory three types of products A, B and C are manufactured. All workers employed in the factory
are equally efficient. In one hour, 100 workers can produce 80 A’s, 160 B’s, 120 C’s. In two hours,
75 workers can produce 125 A’s, 140 B’s and 180 C’s. In three hours, 150 workers can produce 150
A’s, ‘X’ B’s and 540 C’s. What is the value of ‘X’?
(a) 4920
(b) 79
(c) 110
(d) 4500
33.
A box contains 25 red balls and 20 blue balls. An unbiased die is rolled, if the result is an even number,
then 3 red balls and 1 blue ball are taken out from the box without replacement and if the result is an
odd number, then 2 blue balls and 1 red ball are taken out from the box without replacement. If the die
is rolled 4 times, then what is the probability that the total number of red balls, which are taken out, is
more than the number of blue balls, which are taken out ?
7
(a)
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1
2
(b)
5
8
(c)
11
16
2
(d)
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34.
There are two tanks T1 and T2. Two pipes P1 and P2 are used to fill these tanks. When operating alone,
P1 takes 12 hours more to fill T1 than to fill T2, but P2 takes 24 hours more to fill T1 than to fill T2. When
operating together how many hours more, will they take to fill T1 than to fill T2?
(a) 10 hrs
(b) 8 hrs
(c) 7 hrs
(d) 9 hrs
35.
pq, pr, qp and pp are two-digit numbers, ‘pqr’ is a three-digit number and ‘prrp’ is a four-digit number
(p, q, r are all numerals). If pq × pr = pqr, then the remainder when (qp × prrp) is divided by ‘pp’ is
(a) 0
(b) 1
(c) 7
(d) None of these
36.
Three semicircles S1, S2, S3 with radii ‘r’units, ‘2r’ units and ‘4r’ units respectively are drawn with the
same center(O) as shown in the figure given below. From a point M on S3, two tangents MP and MQ are
drawn such that MP is a tangent to S2 and MQ is a tangent to S1. Find the area (in square units) of the
quadrilateral OQMP.
M
P
S3
S2
Q
S1
O
(a)
(c)
r2
(
15 + 2 3
)
(b)
2
r2
(
15 + 8 3
)
(d)
2
r2
(
15 + 4 3
)
2
(
r 2 2 15 + 3
)
2
DIRECTIONS for Questions 37 and 38: Answer the questions on the basis of the information given below.
The average marks obtained by the candidates who passed and those who failed in an examination are 60 and
25 respectively. The average marks obtained by all the candidates who appeared for the examination is more
than 43 but not more than 49.
37.
The number of candidates who passed as a fraction of the total number of candidates who appeared for
the examination could never be
(a)
38.
Page
3
5
(b)
4
7
(c)
18
35
(d)
24
35
The minimum possible total marks obtained by all the candidates in the examination could be
(a) 150
(b) 85
(c) 110
(d) 145
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39.
In the figure given below, AB, BC and CD are tangents to the circle at the points P, Q and R respectively.
If BC = 1 unit and the measures of the ∠ABC and ∠BCD are 120° and 150° respectively, then find the
radius (in units) of the circle.
B Q
C
P
R
A
(a)
3+ 3
4
(b) 1 +
D
1
3
(c)
3
2
(d)
2
3
DIRECTIONS for Questions 40 to 43: Each question is followed by two statements, A and B. Answer each
question using the following instructions:
Mark (a)
if the question cannot be answered even by using both statements together.
Mark (b)
if the question can be answered by using both the statements together, but cannot be answered by
using either statement alone.
Mark (c)
if the question can be answered by using either statement alone.
Mark (d)
if the question can be answered by one of the statements alone, but cannot be answered by using
the other statement alone.
40.
In the figure given below, ABC is an equilateral triangle and points P, Q, R and S are chosen such that
∠QPC = ∠PQR = ∠QRS = 90°. What is the length of CR? (all the dimensions are in cms.)
A: 2 < AB 2 + PQ 2 < 6 and lengths of AB and PQ are both integers.
B: PQ = QR = RS = 1.
A
S
Q
B
41.
Page
R
C
P
It is given that the quadratic equation X2 – PX + Q = 0 has distinct and real roots, where P and Q are
distinct integers. What is the value of (2P + 3Q)?
A: Roots of the given equation are consecutive positive integers and (P, Q < 6).
B: Roots of the given equation are consecutive non-zero integers and (P, Q <6).
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42.
What is the remainder when a five-digit number PQRSR is divided by 125?
(P, Q, S and R are distinct digits.)
A: A =
( PQSR )
and A when divided by 25 leaves a remainder 13.
4
B: RS = SR and when a two digit number QR is divided by 10, the remainder is greater than 3.
43.
Three friends A, G and S calculated their savings. It was found that the savings of A and G were in the
ratio 1 : 2. What was the saving of A?
A: If S lends one-third of his savings to A, and one-third of the remaining to G, he will be left with the
same amount of savings as A will have after receiving one third of the savings of S.
B: If S lends one-fourth of his savings to G and one-fourth of the remaining to A, then the savings left
with him is Rs. 17,000 more than the initial savings of G.
44.
The altitudes PL, QM and RN of the scalene ∆PQR, intersect at a point O inside the triangle.
If PO = 9 units, PL = 10 units, QO = 6 units, then what is the length of QM?
(a) 8 units
(b) 7.5 units
(c) 10 units
(d) 9 units
45.
If 2log8 x + 4log64 y + 6log512 z ≥ 2, then the minimum possible value of (x2y + y2 z + z2x) is
(a) 12
(b) 192
(c) 24
(d) 512
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SECTION – III
DATA INTERPRETATION
DIRECTION for questions 46 to 49: Read the information given below carefully and answer the following
questions.
In the year 2008, the total worth of the assets of the members (A, B, C, D, E and F) of a certain family was
Rs.25 crores. ‘Cash’, ‘Property’, ‘Jewellery’ and ‘Shares’ were the four forms of assets held by the members
of the family. The table given below provides information about the percentage break-up of each form of the
assets held by the members as a percentage of the total worth of the respective forms of assets with the family
in the year 2008.
Members
A
B
C
D
E
F
Cash
20%
18%
21%
10%
25%
6%
Property Jewellery
15%
10%
35%
10%
8%
15%
12%
25%
5%
20%
25%
20%
Shares
25%
12%
10%
20%
18%
15%
46.
In the year 2008, if the total worth ( in Rs. crores) of ‘Cash’, ‘Property’, ‘Jewellery’ and ‘Shares’ was in
the ratio 3 : 4 : 2 : 1, then which member of the family possessed the second highest total worth
( in Rs. crores) of assets excluding ‘Cash’?
(a) F
(b) B
(c) A
(d) E
47.
In the year 2008, if the total worth ( in Rs. crores) of ‘Property’ and ‘Shares’ held by A was the same,
then for how many members of the family, the worth ( in Rs. crores) of ‘Shares’ was less than that of
‘Property’?
(a) 5
(b) 3
(c) 4
(d) 2
Additional Information for questions 48 and 49:
In the year 2009, the total worth ( in Rs. crores) of ‘Property’ held by B decreases by 10%, but that of ‘Shares’
held by B increases by 8%. The total worth of all the other forms of assets held by B remains the same. Also,
the total worth ( in Rs. crores) of all the forms of assets held by all the other members remains the same in the
year 2009. The total worth of the assets with the members of the family increases by Rs. 20 lakhs in the year
2009.
48.
In the year 2008, for how many members of the family, the worth ( in Rs. crores) of ‘Shares’ was
definitely more than that of the ‘Property’?
(a) 6
(b) 3
(c) 5
(d) 4
49.
If the total worth of ‘property’ was an integral multiple of Rs.1 crore in the year 2008, then difference
in the total worth (in Rs.crore) of ‘Property’ and Shares (in 2008) was closest to
(a) 22
(b) 22.5
(c) Data Inconsistent (d) None of these
Page
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DIRECTIONS for Questions 50 to 53: Answer the questions on the basis of the information given below.
The six lead characters of popular sitcom ‘Friends’ were rated by a panel of 4 judges. From every judge, each
character received a distinct integral rating ranging from 1 to 6, depending on how much the character was
liked by that judge, i.e. the character he liked most, was given a rating of 6 and the character he liked least was
given a rating of 1 and so on. The six characters were named Chandler, Joey, Monica, Phoebe, Rachel and
Ross. The judges were named J1, J2, J3 and J4.
Further information is given below:
1. Chandler received a different rating from each judge. This holds true for the other five characters as well.
2. For each of Chandler, Monica and Rachel the ratings received from the four judges were in A.P.
3. The sums of four ratings received by Chandler, Monica and Rachel were also in A.P., with a common
difference of 4, not necessarily in that order.
4. The sums of four ratings received by Joey, Phoebe and Ross were also in A.P., with a common difference
of 1, not necessarily in that order.
5. The ratings received by Chandler from J2, Monica from J4 and Rachel from J3 were the same.
6. Monica received a higher rating from J3 as compared to what she received from J2.
The following table provides partial information about the ratings received by the six characters from the four
judges.
Chandler
Joey
Monica
Phoebe
Rachel
Ross
J1
6
3
1
2
4
5
J2
J3
J4
4
5
50.
What was the maximum possible sum of the four ratings received by any of the six characters?
(a) 14
(b) 16
(c) 17
(d) 18
51.
What was the sum of the four ratings received by Ross?
(a) 12
(b) 18
(c) 14
(d) None of these
52.
What was the rating received by Monica from J4?
(a) 2
(b) 3
(c) 4
(d) None of these
What was the rating received by Joey from J2?
(a) 1
(b) 3
(c) 6
(d) Cannot be determined
53.
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DIRECTIONS for Questions 54 to 56: Answer the questions on the basis of the information given below.
The following table provides partial details about the number of Tests (T) and ODIs (O) played by
6 players of the Indian cricket team against five nations viz. Australia (A), South Africa (S), England (E),
Pakistan (P) and the West Indies (W) in the year 2008. Assume that the Indian cricket team played only
against these nations in the year 2008, and also, they played no form of matches other than the Tests and the
ODIs. The following pie-chart provides details about the percentage break-up of the matches played by the
Indian cricket team against these nations in the year 2008.
A(25%)
W(30%)
S(20%)
P(10%)
E(15%)
A
T
8
Sachin
Sehwag
Gambhir 11
9
Raina
7
Yuvraj
Dhoni
S
O
11
12
18
16
T
12
E
O
24
T
P
O
11
7
7
8
9
6
T
8
13
14
W
O
12
11
6
9
6
10
10
18
T
O
17
16
18
24
32
11
19
16
54.
The total number of matches played by the Indian cricket team in 2008 could not be less than
(a) 200
(b) 240
(c) 190
(d) 230
55.
Out of the matches played by the Indian cricket team against the West Indies in 2008, the number of
matches not played by Yuvraj could at least be
(a) 18
(b) 9
(c) 22
(d) 21
56.
If Raina played all the “ODIs” and Sachin played all the “Tests” that the Indian cricket team played
against England in 2008, then what could be the minimum number of tests played by the Indian cricket
team against England in the year 2008?
(a) 16
(b) 19
(c) 22
(d) 20
Page
17
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DIRECTIONS for Questions 57 to 60: Answer the questions on the basis of the information given below.
Johnny was very fond of ice creams; however he was very selective about the flavour of the ice cream he ate.
Each ice cream that Johnny ate was one or the other of the seven flavours ‘L’, ‘O’, ‘M’, ‘BS’, ‘C’, ‘BC’ and
‘S’. On each day starting from Sunday to Saturday of a particular week X, he ate three ice creams, each of a
different flavour. Also, in this particular week he ate equal number of ice creams of each of the given flavours.
Additional Information Given:
I.
Whenever he ate flavour L, he did not eat it on the next two days.
II.
He never ate ice creams having flavours ‘C’ and ‘BC’ on the same day, but always ate ice creams
having flavours ‘S’ and ‘BC’ on the same days.
III. There were exactly two non consecutive days in the week in which he ate ice creams having flavours
‘O’ and ‘M’ together.
IV. He did not eat ice cream having flavour ‘L’ with the ice creams having one or the other of the three
flavours ‘C’, ‘M’ and ‘BS’ on any day of the week.
V.
He ate all the three ice creams having flavour ‘BS’ before the day on which he ate the third ice cream
having flavour ‘O’.
57.
On which of the following days of the week X, Johnny definitely ate an ice cream having flavour ‘O’?
(a) Thursday
(b) Monday
(c) Tuesday
(d) Friday
58.
On how many days of the week X, Johnny ate ice creams having flavours ‘S’ and ‘L’ together?
(a) 1
(b) 3
(c) 2
(d) Cannot be determined
59.
For how many days of the week X, all the three flavours of the ice cream eaten by Johnny can be
uniquely determined?
(a) 4
(b) 2
(c) 5
(d) 3
60.
If Johnny did not eat ice cream having flavour ‘O’ on Monday, then on which day of the week X he ate
ice cream of flavour ‘O’ but not ‘M’?
(a) Tuesday
(b) Wednesday
(c) Thursday
(d) Friday
Page
18
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Proctored - Mock CAT 7
Answers and Explanations
Page
1
b
2
c
3
c
4
d
5
a
6
d
7
a
8
b
9
c
10
a
11
d
12
b
13
b
14
c
15
c
16
c
17
d
18
a
19
b
20
a
21
d
22
d
23
b
24
c
25
d
26
b
27
b
28
a
29
d
30
a
31
c
32
a
33
c
34
b
35
a
36
b
37
c
38
d
39
a
40
d
41
d
42
c
43
b
44
b
45
c
46
a
47
b
48
a
49
c
50
d
51
c
52
b
53
d
54
b
55
d
56
c
57
d
58
b
59
a
60
c
1
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1. b
Option (a) is too specific to capture the implication of the
comment. Moreover, it does not talk about economists at whom
the comment is aimed. Option (c) is excessive as we cannot
infer from the comment that a well plumed bird wins in the
end. All we can infer is that the behaviour of a typical economist
is like a well-plumed bird. Option (d) is incorrect as the passage
does not talk about ‘putting down other economists.’ Yes, it
does talk about the uncaring attitude. Hence Option (b) is apt
as it talks about the behaviour of economists which is similar
to well-plumed birds—— aiming to promote their own work.
2. c
The lines in the first para “Mr Leamer, an economist at the
University of California in Los Angeles, was frustrated by
empirical economists’ emphasis on measures of correlation
over underlying questions of cause and effect, such as
whether people who spend more years in school go on to
earn more in later life” reveal that the input variable is the ‘time
spent in school’ and the output is ‘earnings’.
6. d
There should be a ‘that’ or a ‘which’ after ‘companies’ to
represent the idea of a restrictive clause as the use of
sophisticated machinery and production of high quality
products is specific to some companies. Option (a) is incorrect
because it places a comma before ‘which’ and after ‘products’;
in this case it seems as the production of high quality products
and use of sophisticated machinery are being indicated as
additional information about companies that ‘understand the
needs’. In case of the given sentence it is semantically
incorrect. Option (b) contains a subject-verb agreement error.
The subject ‘companies’ is plural so the verb should be
‘understand’. Option (c) uses the -ing form of the verb ‘use’
and does not use the same for ‘produce’. This leads to an
error of parallelism.
7. a
In the first sentence, ‘faze’ means to disturb whereas ‘phase’
refers to a stage in a process of development or an aspect.
‘Phased’ does not fit with the given sentence. The given
sentence refers to the subject’s refusal to be affected by
insulting remarks. In the second sentence, ‘canon’ refers to
laws, principles whereas ‘cannon’ is a part of artillery. The
word ‘equitable’ means fair, impartial or just and ‘equable’
means steady. The third sentence refers to the equal and fair
treatment given to all citizens by the law. The word ‘reign’
means to rule whereas ‘rein’ means to check or stop, control.
The given sentence refers to lawlessness dominating the
city. ‘Inflammable’ is used for something that can be easily set
on fire whereas ‘inflammatory’ refers to something that
provokes anger or hostility. A communal discord can occur
due to inflammatory remarks.
8. b
Taking up option (a), we can see that the purpose of scientific
data generated could not be to portend (to give an omen or
anticipatory sign of). So option (a) cannot be the answer for
the question. Option (b) is the correct answer. The forestalling
(Forestall means to prevent or hinder by doing something
ahead of time) of an inchoate rift makes proper sense. Because
the data will not allow the rift to develop further. The rift is in a
nascent stage and the data from the satellites will stop the
development of the rift. Option (c) is not the correct choice, as
disturbances do not fit the second blank. Option (d) is not the
correct answer. Schism means a separation or division into
factions. One can resolve factionalism but not faction. This
expression is incorrect.
9. c
In Option (a), “... the better it solves them,” creates a doubt:
what does the pronoun ‘them’ denote here? It is incorrect as
it fails to pair with the last line of the paragraph; rather it
follows option (c). Option (b) can be easily annulled, as it is
convoluted and ambiguous due to the phrase, “the seed of its
own negation”. Here, we do not know whether the awareness
of the environment is subject to negation of the mind or the
organism itself is subject to negation. Option (c) is correct as
it aptly forms a pair with the last line of the paragraph and
extends the discussion on the other factor: environment – the
non-ego, which can be interpreted as a riddle; the brainteaser to be understood and solved. Option (d) talks about the
resolution of the oppositeness between ego and environment
although, there is no conflict between the ego and the
environment apparent in the paragraph. One can see that
option (d) may follow option (a) and does not follow the last
line of the paragraph.
Also refer to the lines in the third para “some relevant variables
may simply not be observable. For example, the time someone
stays in school is probably influenced by his innate scholastic
ability, but this is very hard to measure. Leaving such variables
out can easily lead econometricians astray.” So one can infer
that the left out variable is ‘scholastic ability’.
3. c
4. d
5. a
Page
Option (a) is incorrect as the passage does not examine the
role of instrumental variables in “causal literature”. Indeed, the
passage mentions instrumental variables with context to
“causal literature” but then the passage moves on to discuss
the influence of instrumental variables on economics. Option
(b) leaves out ‘instrumental variables’ which is the main topic
of discussion in the passage. Option (d) leaves out
‘economics’ which makes the choice too general and without
a context. Option (c) is correct as the author in the 2 nd
paragraph, in the lines “The techniques…education”, begins
to discuss the influence of instrumental variables on economics;
the author further highlights this influence with the help of
examples like ‘Freakonomics’.
Option (a) is incorrect. Refer to the lines “The techniques at
the heart of this literature–in particular, the use of so-called
“instrumental variables”-have yielded insights into everything
from the link between abortion and crime to the economic
return from education. But these methods are themselves
now coming under attack.” This makes it clear that the
techniques have not received a unanimous acceptance. Option
(b) is incorrect as instrumental variables affect the output
through their influence only on the input variable. Refer to
para 4. Option (c) cannot be inferred as the instrumental
variable created by Joshua and Alan ‘ teases out’ schooling’s
true effect on wages. This means that the instrumental variable
carefully separates out ‘schooling’s true effect on wages’
from a host of related factors or variables. This does not
mean that years of schooling have no effect on the wages
earned after schooling.
In the question, filling the second blank holds a very important
key. It says that in the process of throwing off the shackles
we are now exposed to the dangers of incipient theories and
solutions. On the basis of this, we can eliminate options (b)
and (c). Now out of the remaining two options, we can
eliminate option (d) on the basis of the first word-’impervious’
(not allowing entrance or passage), which does not fit in the
first blank.
2
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10. a
Option (b) can be inferred from the line in Para 1 “Instead, that
country is viewed either with ignorant disapproval’ or with
uncritical admiration”. Option (c) can be inferred from the line
in Para 2 “if only animals became aware of their strength, we
should have no power over them, and that men exploit animals
in much the same way as the rich exploit the proletariat.” This
can be extended to the rich and proletariat. Option (d) can be
inferred from the fact that Orwell has represented the
capitalists with Mr. Jones whose nature is self- indulgent and
uncaring. But option (a) cannot be inferred as the statement is
generalized. In the passage the statement is specific to
England.
11. d
An ‘objective’ tone is seen when the author quotes what
Orwell has written. Narration is predominant throughout the
passage as the author relates what Orwell has written. For
example, “Orwell begins his book by criticizing the
capitalists…etc.” The author also describes certain entities,
for example “Boxer, the overworked, incredibly strong, dumb
horse represents the common worker in Russia.” But the
author is not critical of anything. He is merely stating Orwell’s
opinion. The author does not take any particular side in the
passage. He objectively quotes, narrates or describes what
Orwell has written.
12. b
13. b
14. c
Page
‘C’ occurs first in sequence as seen in the first paragraph
where the humans are seen to be the exploiters. ‘B’ occurs
next as seen in Para 1 where “Old Major” tells the other
animals about his dream of “animalism” and the other animals
actually implement it. D occurs next as seen in the first line of
Para 2 where Napolean drives out Snowball. ‘A’ occurs last
as the class that revolted (the pigs) acquires a resemblance
to humans.
Secular means of or relating to the worldly or temporal.
Mundane also means of, relating to, or typical of this world;
secular. Preposterous means contrary to nature, reason, or
common sense; absurd. Prudent means marked by wisdom
or judiciousness. Fugacious and transient mean lasting for a
short time. Recalcitrant means obstinately defiant of authority
or restraint. Authoritative means having or proceeding from
authority. Patent means open to public inspection.
The question states that if the people are dissuaded from
using petrol then they will use less petrol and this will earn
less money for fertilizer subsidy. So if the objective of the first
is achieved then the objective of second will be jeopardized
(due to lack of funds). Option (a) cannot be the answer. If the
books are returned on time(which is the objective of sending
reminders), then there will be no need to send the reminders.
So, success of first does not jeopardize the success of the
second. Option (b) cannot be the answer as the achievement
of the objective of the first will definitely lead to achievement
of the objective of the second. Option (c) is the correct
answer. If people are dissuaded from using the metro service,
then the funds for the expansion of metro services will be
jeopardized. Hence, achievement of the objective of the first
will lead to difficulty in achieving the objectives of the second.
Option (d) cannot be the answer. The reasoning is similar to
that of option (a). If there is no litter, then there will be no need
to pay overtime to the workers.
3
15. c
Options (a) and (b) discuss the role of designs in everyday
life while the author has moved on to explain the obsession of
the rich with the excesses of neo-classical designs. Hence,
these options do not seem to be an appropriate ending for the
paragraph. Option (c) is the best choice because the keywords
‘excesses of neo-classical architecture’ and ‘less is more’
refer to the idea of grandeur associated with acceptable
designs among the rich. This statement also reveals the motive
behind choosing excessive designs and hence is an apt
choice. Option (d) reiterates the bizarreness of popular
designs whereas the last sentence of the paragraph refers
specifically to the obsession of the rich with ‘neo-classical
designs’.
16. c
Option (a) is incorrect because ‘things’ is plural and countable
and it should be preceded by ‘many’ and not ‘much’. Also, the
last part of the sentence uses future continuous tense
whereas the sentence is in present tense. Option (b) contains
two errors. First, ‘things’ is plural, so ‘are’ should be used.
Second, in the last part of the sentence ‘must be finding’ is
incorrect. Option (c) is the best choice because it does not
contain any error.
In option (d) the adverb ‘generally’ has been incorrectly placed
without a comma before the noun ‘research’.
17. d
The question statement clearly mentions the word melancholy
(depression of spirits). From this we can infer that the previous
blank should be filled with an antonym of the word. So, blitheful,
blissful and cheerful can be used. ‘Fleetingness’ would fit the
second blank as the ‘profound melancholy’ can arise out of a
transitory or fleeting nature of natural beauty and human glory.
18. a
Option (a) is the correct answer. It can be seen that the
professor is generalizing about all graduate students but he
has data only of his students. This is a major flaw in the
argument. Option (b) makes an assumption that the argument
pertains to English language, which is incorrect. Option (c) is
beyond the scope of the argument. Option (d) is incorrect as
the argument does not pass any judgement on the capability
of the teacher.
19. b
Formation means an arrangement of a body or group of people
or things in some prescribed manner or for a particular purpose.
Soldiers are arranged in a formation. Club means an association
of people for some common object usually jointly supported
and meeting periodically. A matrix consists of rows and
columns but it is not a formation of columns; a matrix may be
a formation of numbers or alphabets. Array means a number
of mathematical elements arranged in rows and columns. A
forest is a dense growth of trees, but not a formation of trees.
20. a
Here, option (a) is the appropriate idiomatic expression. In
option (c), “raking over the coals” which means to talk about
unpleasant things from the past that other people would prefer
not to talk about, is out of context. In option (b), “to take a
running jump” which is an impolite way of telling someone to
go away or that you will not give them something they want,
is again unneeded and hence negated. In option (a), “ carrying
coals to Newcastle” which means to take something to a
place or a person that has a lot of that thing already, does the
needful for the given sentence. In option (d), if you have “a
running battle” with someone, you have an argument that
continues over a long period of time. In the present context,
no extended argument or conflict has been hinted at.
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21. d
22. d
23. b
24. c
The passage clearly hints at a conflict or misunderstanding
between the parents and the child. Refer to the last line,
which states, “I was learning…breaking”. Option (a) makes
an abrupt shift from this as it says ‘…our parents can easily
identify’. Options (b) and (c) are ruled out as these options
fail to match with the tone of the last two lines of the paragraph,
in which the speaker talks about his/her past experiences as
a child. Refer to the lines, “... I was learning that parents
weren’t always right...we all go through at least a little
rebellion.” Option (d) is better equipped than any other option
given. It reveals the speaker’s past experiences as a child
controlling and steering its emotions, thoughts and energy.
In the first line of the last paragraph, the author mentions that
“ if turning away from the outer world is accepted as the
decisive case of the most conspicuous characteristics of our
dreams”; this in no manner implies that turning away from the
outer world leads to dreams. Option (c) cannot be inferred
from the passage. Dissonance experienced with others can
be one of the sources of the reckless extravagances of our
judgements, hopes and wishes in dreams and not a cause of
dreams. Even though, the passage states that lack of sensory
stimuli leads to sleep we do not know what happens when a
sleeping mind is excited by sensory stimuli, thus even option
(b) cannot be inferred.
Statement A is given in the passage. Refer to the lines, “ He
states the first distinguishing mark of dreams…perceptions”
in the first paragraph. Statement B is also shown to be linked
to mistaking hallucinations for objective perceptions in dreams.
Refer to the following lines in the first paragraph, “ These
activities too, …..during sleep”. Statement C is mentioned in a
different context and talks about a new idea.
Option (a) is inappropriate as the author just discusses
Haffner’s explanation. He does not show how Haffner’s
explanation is different from Delboeuf’s. The author moves on
to give more clarity and also to moderate the deductions made.
Option (b) is also narrow. It does not talk about ‘Burdach’ or
the author attempting to give more clarity in the latter part of
the passage. Option (d) is also incomplete as it only talks
about ‘moderation’ as the aim in moving to Burdach’s
observations. Only option (c) represents without an error
how the author develops the passage.
27. b
1366 – 23
1366 − 23
1366 – 1 – 22 (133 )22 − 1 − 22
= 2
=
=
183
13 + 13 + 1 132 + 13 + 1
132 + 13 + 1
(13 – 1) (133 )22 – 1 – 22 (13 – 1) (133 )22 – 1 – 22

=


(13 – 1)(132 + 13 + 1)
(133 – 1)
[(133)22 – 1 is divisible by 133 – 1.]
Therefore, the net remainder = 183 – 22 = 161.
Alternative method:
Dividend 1366 – 23 is of the form 3k + 2 (where k is a natural
number) and the divisor 183 is a multiple of 3. Therefore, the
remainder has to be of the form 3N + 2 (where N is a natural
number) and of the given options only 161 is of such a form.
28. a
We obtain the sum of all the coefficients of a polynomial by
equating all the variables to 1. Here by putting x = 1 in the
polynomial, the required sum comes out to be zero.
29. d
It is given that, a = b3/2 and c = d5/4
As a and c are positive integers, b has to be a perfect square
and d has to be fourth power of a natural number.
Let, b = x2 and d = y4, where x, y are positive integers.
b – d = x2 – y4 = (x – y2) (x + y2) = 9.
⇒ (x – y2), (x + y2) = 1, 9
i.e. x = 5, y = 2
or a – c = x3 – y5 = 125 – 32 = 93.
30. a
As we have only 3-digit and 4-digit numbers in the set G, a
particular category can have either 1 digit or 2 digits or 3 digits
or at the most 4 distinct digits. Number of categories of 1 digit
= 9C1 = 9 (we cannot consider zero in this case).
Number of categories of 2 digits, 3 digits and 4 digits would be
10
C2, 10C3 and 10C4 respectively. Therefore the required answer
is 9C1 + 10C2 + 10C3 + 10C4 = 384.
31. c
(7 – a) × (7 – b) × (7 – c) × (7 – d) × (7 – e) = 28.
Since, (7 – a), (7 – b), (7 – c), (7 – d), (7 – e) are all distinct
integers, 28 can be written as 1 × 2 × 7 × (– 2) × ( – 1).
Hence, the values that a, b, c, d and e can take, are 6, 5, 0, 9
and 8 in any particular order.
But for each of these cases the sum a + b + c + d + e is
always 28.
25. d
In option (a), “Old heave-hos” is the act of throwing someone
out; dismissal from one’s job or from one’s position. “An open
sesame” is a very successful way of achieving something. In
option (c), “old flame” is a person that you loved or had a
romantic relationship with in the past. Thus, for the given
sentence options (a), (b) and (c) are unsuitable. The correct
answer choice is (d). “Eat carrots for better eyesight” is an
old wives’ tale- an often traditional belief that is not based on
fact.
32. a
Let each worker put in 1 unit of work per hour. Let, it take a, b
and c units of work to produce one unit of the products A, B
and C respectively.
So, 100 = 80 a + 160 b + 120 c
...(i)
150 = 125 a + 140 b + 180 c
...(ii)
450 = 150a + X b + 540 c
...(iii)
Solving for (1.5 (i) – (ii)) gives the relation, A = 20 B.
Substituting, a = 20 b in (3 (ii) – (iii))
We get X = 4920.
26. b
Let us write first ‘260’ natural numbers. Our task is to find
those numbers that are either squares or cubes of a natural
number and eliminate them from the series.
33. c
The probability of getting an odd or even result on rolling a die
There will be  260  = 16 perfect squares and  3 260  = 6
perfect cubes, ([ ] is the greatest integer function.)
Also, there are two numbers (1 and 64), that are both a
perfect square and a perfect cube. So, altogether 16 + 6 – 2
or 20 numbers will get eliminated. Hence, 260 will be 260 – 20
= 240th term of the set ‘S’.
1
.
2
Let O = Odd, E = even.
Following are the possible cases:
is the same and it is
I.
When we have 2 even and 2 odd results
Number of red balls taken out = 3 + 3 + 1 + 1 = 8.
Number of blue balls taken out = 1 + 1 + 2 + 2 = 6.
This satisfies our requirement and this is possible in
4
2 2
= 6 cases.
Page
4
MBA
Test Prep
Proctored - Mock CAT 7
II.
The cases are: (OOEE), (OEOE), (EEOO), (EOEO), (OEEO)
and (EOOE).
So, PM = OM2 − OP2 or
When we have 3 even and 1 odd result, total cases
Area of ∆OPM = × PM × OP = × 2 3r × 2r = 2 3r 2 square units.
1
2
4!
= 4.
3!
III. When we have ‘4’ even and ‘0’ odd results, total cases
=
4!
= 1.
4!
Total number of cases satisfying the criteria = 6 + 4 + 1
= 11.
Total number of cases = 24 = 16.
⇒ Area of ∆OQM =
T1 − T2
= 12,
P1
T1 − T2
= 24,
P2
(T – T2 ) (T1 – T2 )
⇒ P1 + P2 = 1
+
12
24

 (T1 − T2 )
T1
T2
Required answer = 
−
=
 (P1 + P2 ) (P1 + P2 )  (P1 + P2 )
=
1
= 8 hours.
1
1
+
12 24
1
2
15 2
r square units.
2
Hence, area of quadrilateral OPMQ=
11
∴ Required probability = .
16
Let T1 m3 and T2 m3 be the capacities of the two tanks and
P1 m3/hour and P2 m3/hour be the flow rates of the two pipes P1
and P2.
(
Since, pq × pr = pqr
⇒ pq × pr = 10 × pq + r
⇒ pq(10 – pr) + r = 0
Here, there are two possibilities.
I. pq(10 – pr) = – r
3 r is single digit number and pq is a two-digit number,
2
∴ 43 <
square
60p + 25f
≤ 49
p+f
⇒
11
17
11 f 17
p≤f <
p⇒
≤ <
24
18
24 p 18
⇒
11
f
17
+ 1≤ + 1<
+1
24
p
18
⇒
35 f + p 35
≤
<
24
p
18
⇒
18
p
24
.
<
≤
35 f + p 35
37. c
38. d
⇒ pq(10 – pr) = 0, pr = 10 (as pq ≠ 0 ).
⇒ p = 1,
∴ The required remainder is the number which we get
as the remainder when q1 × 1001 is divided by 11.
1 1
< .
a b
The required fraction will always be greater than
less then or equal to
pq(10 – pr) = r = 0
18
and
35
24
.
35
In order to minimize the total marks obtained by the candidates,
we should minimize the number of candidates. We can infer
from the given information that the number of students who
passed the test is more than those who failed in it as the
average marks of all the candidates is nearer to 60 in
comparison with 25. If we take two students who passed
and one who failed, their average marks
36. b
) r2
For questions 37 and 38:
Let, the number of candidates who passed in the examination be 'p'
and the number of candidates who failed in the examination be ‘f’.
this is impossible if r ≠ 0 .
II.
15 + 4 3
units.
Note: For positive numbers a and b if a > b then
35. a
or 2 3 r units .
Similarly, MQ is a tangent to the semicircle S1.
So, ∠OQM = 90° .
=
34. b
( 4r )2 − (2r )2
60 × 2 + 25
fulfils
3
M
145
≤ 49 . Therefore the minimum total
3
marks can be 60 × 2 + 25 = 145.
the condition as 43 <
P
Q
S3
S2
S1
O
Join MO.
Area of the quadrilateral OPMQ is equal to the sum of the
areas of ∆OPM and ∆OQM .
Since, PM is a tangent, therefore ∠OPM = 90°
Page
5
MBA
Test Prep
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39. a
Statement II:
PQ = 1
So, in triangle QBP
Extend AB and DC to intersect at the point S.
Let the radius of the circle be ‘r’ units.
S
B
PQ
2
=
sin60°
3
Also WX = SR = PQ = 1
So, in triangle WQX
QB =
C
Q
P
R
O
WQ =
D
A
WX
2
=
sin 60°
3
and QX =
∠CBS = 180° − 120° = 60° and ∠BCS = 180° − 150° = 30° .
WX
1
.
=
tan60°
3
⇒ ∠BSC = 180° − (60° + 30°) = 90° .
Also, WS = XR = QR − QX =
∴ ∠PSR = ∠SPO = ∠POR = ∠SRO = 90° and OP = OR .
∴ PSRO is a square.
1
.
2
=
2
2
+
+
3
3
In ∆PBO : ∠PBO = 60° (3 ∆OPB and ∆OQB are congruent.)
CR =
PO
= tan60° = 3
PB
3+ 3
⇒
= 3 ⇒r =
.
1
4
r−
2
r
S
W
3
(CY
2
(
)=
3 −1
3
(as WS is
3 +1
) ((BC − BY )
2
+ RY 2 =
=
((AB − BY )
=
((AB − QR − BP)
2
+ (PQ )
2
2
+ (PQ )
2
)
) = ((AB − PY − BP)
2
+ (PQ )
2
+ (PQ )
2
)
)
2


1 
=  3 + 1− 1−
+ 12  =



3


A
40. d
) = AW
3 −1
parallel to QR and hence BC, AWS must also be an
equilateral triangle).
So, AB = BQ + QW + WA
BS
1
= sin30° ⇒ BS = .
BC
2
∴ BP = r −
(
7
.
3
So, Statement II alone is sufficient.
41. d
Q
R
Let a and a + 1 be the real and distinct roots of the given
equation.
X
B
P
Y
C
Lets draw WS parallel to QR and then WX parallel to SR.
Also extend SR to meet BC at Y.
Statement I:
2 < AB 2 + PQ 2 < 6 and lengths of sides AB and PQ (in cms)
are integers.
⇒ AB = 1 or 2
But if ‘AB = 1 cm’ then PQ is definitely less than 1 and AB2 +
PQ2 < 2 which goes against the statement.
So, AB = 2 cm.
Subsequently PQ can only be 1 cm.
As no relation between PQ , QR and SR is provided, we can
say that there are many cases that may satisfy the above
condition. And hence many distinct locations of point R are
possible.
So, statement I alone is insufficient.
Page
6
From Statement A:
Sum of the roots = a + a + 1 = P;
Product of the roots = (a) x (a + 1) = Q
Only possible value Q can take such that the roots of the
equation are consecutive positive integers is 2 (otherwise Q
will become greater than or equal to 6), where the roots of the
equation are 1 and 2.
Hence, P = 3 and Q =2.
Therefore, (2P + 3Q) = 12.
Statement A alone is sufficient to answer the question.
From Statement B:
Let b and b + 1 be the real and distinct roots of the given
equation.
Sum of the roots = b + b + 1 = 2b + 1 = P
Product of the roots = b × (b + 1) = Q
Only possible value Q can take such that the roots of the
equation are consecutive non-zero integers is 2 (otherwise
Q will become greater than or equal to 6); where the roots
of the equation can be (–1, –2) or (1, 2).
If the roots of the equation are (–1, –2) then
P = –3 and Q = 2 and 2P + 3Q = –6 + 6 = 0.
If the roots of the equation are (1, 2) then
P = 3 and Q = 2 and 2P + 3Q = 6 + 6 = 12.
Hence statement B alone is not sufficient to answer the
question.
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42. c
The remainder when a five-digit number PQRSR is divided by
125 is same as when a three-digit number RSR is divided by
125.
So, if we can find unique values of R and S, we can find the
answer to the question.
Hence, the question can be answered by using both the
statements together.
44. b
P
From Statement A:
A = 25K + 13 (K is a natural number.)
PQSR = 4A = 4 (25K + 13) = 100K + 52.
⇒ S = 5 and R = 2.
Hence statement A alone is sufficient to answer the question.
O
From Statement B:
QR leaves a remainder greater than 3, when divided by 10.
So, R has to be greater than 3.
Also, given that RS = SR, so the values of R and S have to be
4 and 2 respectively.
Hence, the remainder can be found.
Hence, statement B alone is also sufficient to answer the
question.
43. b
Q
∠OLQ = ∠OMP.
QO OL
=
PO OM
⇒ QO × OM = PO × OL
⇒ QO + (QM – QO) = PO × (PL – PO)
⇒ 6 (QM – 6) = 9 (10 – 9)
Therefore, we get:
⇒ QM = 7.5 units.
1
1 2
s to A and × s to G.
3
3 3
45. c
2  
1 
1
∴ s −  s + s =  a + s 
9  
3 
3
s
9
Nothing can be said about the savings of S. So, this statement
alone is not sufficient to answer the question.
⇒ log8 ( xyz ) ≥ 2
2
⇒ (xyz)2 ≥ 64
⇒ (xyz) ≥ 8 (3 (xyz) is positive.)
⇒ (xyz)3 ≥ 512
From Statement B:
Let the savings of S and G be ‘s’ and ‘g’ respectively.
(
)(
)
Applying AM ≥ GM, we get that
(
x 2 y + y 2 z + z2 x
≥ x 2 y ⋅ y 2 z ⋅ z2 x
3
3 
1
∴s −  s +
s  = 17000 + g
16 
4
9
s − g = 17000
16
Nothing can be said about the savings of S. Hence, this
statement alone is also not sufficient to answer the question.
46. a
The total worth (in Rs. crores) of ‘Property’, ‘Jewellery’ and
‘Shares’ are
M e m be r s Total w or th of as s e t (Excluding cas h)
...(ii)
A
Rs.2.625 crores
9
s − 2a = 17000
⇒
16
B
Rs.4.3 crores
C
Rs.1.8 crores
s
From statement A, we get a =
9
D
Rs.2.95 crores
9
2
s − s = 17000
16
9
7
E
Rs.1.95 crores
F
Rs.3.875 crores
Of course, the required worth was the second highest for
F.
17000 × 144
⇒ s=
49
∴ a=
1
3
 4
  2

 1

 (25 ) = 10  ,  (25 ) = 5  and  (25 ) = 2.5 
 10
  10

 10

Combining both the statements together:
Since, it is known that the ratio of savings of A and G is 1 : 2.
Hence, a : g :: 1 : 2 or g = 2a
...(i)
⇒
)
⇒ x 2 y + y 2 z + x 2 z ≥ 24
⇒ Minimum possible value of (x2 y + y2 z + z2 x) = 24.
⇒
9
s − g = 17000
16
)(
2
2
2
⇒ x y ⋅ y z ⋅ z x ≥ 8.8.8.
1
1 3
So, S must have given s to G and × s to A.
4
4 4
Page
3 2log8 x + 4log64 y + 6log512z ≥ 2
⇒ log8 x2 + log8 y2 + log8 z2 ≥ 2
⇒ a=
From Statement (B), we get
R
L
Triangles QOL and POM are similar. Since, ∠POM = ∠QOL and
From Statement A:
Let the savings of S and A be ‘s’ and ‘a’ respectively.
So, S must have given
M
N
1
17000 × 16
×s =
9
49
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47. b
Let the total worth (in Rs. crores) of Property and Shares be
‘P’ and ‘S’ respectively.
Given that, 15% of P = 25% of S
S
= 0.6
P
Let ‘M’ denote the ratio of the total worth (in Rs. crores) of
Shares and Property held by each member of the family.
The value of ‘M’ for B, C, D, E and F are
⇒
12  
10  
20  
18 
15 


 0.6 ×
 ,  0.6 ×  ,  0.6 ×
 ,  0.6 ×  and  0.6 ×

35  
8 
12  
5 
25 


respectively.
Therefore, the value of ‘M’ is less than 1 for the members B, C
and F.
For questions 48 and 49:
The total increase in the worth of all the forms of assets held by the
members of the family = Rs. 20 lakhs.
The decrease in the worth (in Rs. crores) of the Property and the
increase in the worth (in Rs. crores) of the Shares held by B in the
year 2009 as compared to the year 2008 are 0.1 × 0.35P and
0.08 × 0.12S respectively.
So, we can say that 0.08 × 0.12S > 0.1 × 0.35P.
S 175
⇒ 96S > 350P ⇒ >
( = 3.65 ).
P 48
48. a
In 2008, the worth ( in Rs. crores) of the Shares is greater
than that of the Property for all the members of the family.
49. c
Since, it is given that
0.08 × 0.12S – 0.1 × 0.35P = 0.2 (in Rs. crores)
⇒ 48S – 175P = 1000
1000 175P
+
= 20.83 + 3.65P
48
48
Only possible value P can take = Rs.1 crore
(as otherwise the value of S will go beyond Rs. 25 crores).
⇒ S = 20.83 + 3.65 = 24.48 crores.
But in this case S + P = 24.48 + 1 = 25.48
But 25.48 is greater than 25 and this is impossible (as the total
worth of assets in 2008 was 25 crores).
Hence, P cannot be a multiple of a crore.
⇒ S=
For questions 50 to 53:
The maximum possible sum of ratings received by a character
(considering only statement 1) could be when he/she would have
received ratings 3, 4, 5 and 6 from the four judges.
Hence, the maximum possible sum = 3 + 4 + 5 + 6 = 18.
The minimum possible sum could have been, ( considering only
statement 1) when a character would have received ratings 1, 2, 3
and 4 from the four judges.
Hence, the minimum possible sum = 1 + 2 + 3 + 4 = 10
Hence, maximum possible difference between the sum of ratings that
can be received by any two characters =18 – 10 = 8.
From statements 2 and 3:
The sum of ratings received by Chandler, Monica and Rachel must be
10, 14 and 18(not necessarily in that order) as no other values can
satisfy the above conclusion.
Since, the four ratings for each of Chandler, Monica and Rachel were
in A.P., sum of ‘14’ can be obtained by 2 + 3 + 4 + 5.
But, Chandler received rating ‘6’ from J1 and Monica received rating ‘1’
from J1.
So, the sum of ratings for Chandler must be 18 (as only 18 can have
a 6 in it) and, the sum of ratings for Monica must be 10 (as only 10 can
have a 1 in it).
Page
8
Hence, the sum of ratings for Rachel was 14.
It is to be noted that, these three have ratings 4 and 3 in common.
From Statement 5:
The ratings received by Chandler from J2, Monica from J4 and Rachel
from J3 must be equal to 3 as rating received by Chandler from J4 is
equal to 4.
Also, Statement 6 means that the ratings received by Monica from J3
and J2 must be equal to 4 and 2 respectively.
From all the above conclusions, the rating received by Chandler, Rachel
and Monica from all the four judges can be concluded as below.
The other possible unknown values are also represented below:
J1
Chandler
6
Joey
3
Monica
1
J2
J3
J4
3
5
4
1 or 4 or 6
1 or 2 or 6
5
2
4
3
Pheobe
2
1 or 4 or 6
1 or 6
1 or 6
Rachael
4
5
3
2
Ross
5
1 or 4 or 6
1 or 2 or 6 1 or 6
From Statement 4:
Let, the sum of four ratings received by Joey, Phoebe and Ross be
(x – 1), x and (x + 1) (not necessarily in that order).
So, (x – 1 + x + x + 1) = 3x.
= (Total sum of ratings) – (Sum of the ratings received by Rachel,
Chandler and Monica) = 4(1 + 2 + 3 + 4 + 5 + 6) – (10 + 14 + 18) = 42.
So, x = 14 and the ratings = 13, 14 and 15.
It can be seen that Ross could not have received rating 4 from J2 as,
his/her sum of ratings could never be 13, 14 or 15.
This is explained below:
If Ross would have received rating 4 from J2, then possible pair of
ratings from J3 and J4: (1,6) or (2,6) or (2,1) or (6,1). So, sum would
have been 16, 17, 12 or 16.
So, Ross received either rating 1 or 6 from J2 and J4 in any order.
Hence, he received the rating 2 from J3.
Ross’ sum of ratings = 5 + 2 + 1 + 6 = 14.
Phoebe received 4 as rating from J2 as she received ratings 1 and 6
from J3 and J4 (not necessarily in that order).
Phoebe’s sum of ratings = 2 + 4 + 1 + 6 = 13.
So, Joey’s sum of Ratings = 15.
It can be concluded that Joey received rating 1 and 6 from J2 and J3
(not necessarily in that order).
The final representation can be as follows:
Chandler
J1
6
J2
3
J3
5
J4
4
Joey
3
1,6
6,1
5
2
4
3
6,1
Monica
1
Phoebe
2
4
1,6
Rachel
4
5
3
2
Ross
5
6,1
2
1,6
50. d
Chandler received 18.
51. c
Ross got 5 + 2 + 6 + 1 = 14.
52. b
53. d
Joey received either of the two ratings 1 or 6 from J2.
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For questions 54 to 56:
Against Australia, Yuvraj played 18 ODIs and Gambhir played 11 Tests.
So, India played at least 18 + 11 = 29 matches against Australia.
Similarly we can say that India played at least 24 + 12 = 36 matches
against South Africa, at least 14 + 18 = 32 matches against England, at
least 12 + 11 = 23 matches against Pakistan and at least 19 + 32 = 51
matches against the West Indies.
Let the total number of matches played by Indian cricket team in 2008
be x.
⇒ India played
x
x
matches with Australia,
matches with South
4
5
3x
x
matches with England,
matches with Pakistan and
Africa,
20
10
3x
matches with the West Indies.
10
⇒ x should be a multiple of 4, 5, 10 and 20.
⇒ x should be a multiple of 20.
As India played at least 29 matches against Australia (against whom
it played 25% of all its matches in 2008)
x
≥ 29 or, x ≥ 116.
4
Similarly
x
3x
≥ 36 or, x ≥ 180,
≥ 32 or, x ≥ 213.33,
5
20
From statement V:
It is obvious that, ‘BS’ was eaten on Monday, Tuesday and Thursday.
Flavour ‘O’ was eaten on Friday.
Johnny could not eat ice creams of flavours L, BC, S and BS on Friday
as they were all exhausted on the other days.
Therefore, on Friday Johnny ate ice creams of flavours ‘O’, ‘M’ and ‘C’.
Following are the cases possible:
Case I:
Flavours ‘O’ and ‘M’ on Tuesday and Friday.
Days
Sunday
L
BC
S
Monday
C
BS
M/O
Tuesday
O
M
BS
Wednesday
L
BC
S
Thursday
C
BS
O/M
Friday
O
M
C
Saturday
L
BC
S
Flavours
Case II:
Flavours ‘O’ and ‘M’ on Monday and Friday.
x
3x
≥ 23 or, x ≥ 230 and
≥ 51or, x ≥ 170.
10
10
But x has to be an integral multiple of 20 and hence the least possible
value of x is 240.
Days
Sunday
L
Flavours
BC
S
Monday
O
M
BS
Tuesday
C
BS
M/O
54. b
Wednesday
L
BC
S
Thursday
C
BS
O/M
Friday
O
M
C
Saturday
L
BC
S
3
= 72 matches against the West
10
Indies in 2008, out of which Yuvraj played 32 + 19 = 51
matches.
⇒ Yuvraj definitely did not play in at least 72 – 51 = 21 matches
against the West Indies in 2008.
India played at least 240 ×
55. d
56. c
Since Raina played all the ODIs against England in 2008,
therefore India played a total of 14 ODIs against England in
3
2008. As we know that India played at least 240 ×
= 36
20
matches against England that year, it must have played at
least 36 – 14 = 22 Test matches against England.
57. d
58. b
59. a
As we can observe in cases I and II, we can uniquely
determine the flavours for Sunday, Wednesday, Friday and
Saturday.
60. c
Given that he did not eat ice cream having flavour ‘O’ on
Monday. So, the only possibility is given below.
For questions 57 to 60:
From additional information (I), we can conclude that Johnny ate ice
cream having flavour ‘L’ on Sunday, Wednesday and Saturday.
From additional information (II) and (IV), we can conclude that he ate
ice creams having flavours ‘L’, ‘S’ and ‘BC’ on Sunday, Wednesday
and Saturday.
The table looks like:
Days
Sunday
L
Flavour s
BC
S
L
BC
S
L
BC
S
Flavours
Days
Sunday
L
BC
S
Monday
C
BS
M
Tuesday
O
M
BS
Wednesday
L
BC
S
Thursday
C
BS
O
Friday
O
M
C
Saturday
L
BC
S
M onday
Tue s day
We dne s day
Thur s day
Fr iday
Satur day
Page
9
MBA
Test Prep
Proctored - Mock CAT 7