MBMAT Mock Test 1 Solutions
Verbal Ability
Critical Reasoning
1.
The correct answer choice is (B).
The conclusion of the argument is the first sentence: “George Orwell’s book 1984 has exercised much influence on a
great number of this newspaper’s readers.” The basis for this conclusion is that 1984 was the second most named book
in a survey about influential books. The argument contains a serious error: just because 1984 came in second in the
survey does not mean that “a great number” of readers selected it as influential. To illustrate this proposition, consider
the following example: Number of people surveyed = 1000, Number of people naming the Bible as the most influential
book = 999, Number of people naming 1984 as the most influential book = 1, In this example, 1984 has come in second,
but no one would say this second place finish supports a conclusion that “1984 has exercised much influence on a great
number of this newspaper’s readers.” You can expect the correct answer to address this issue.
Answer choice (A): The survey in the argument asks readers to name the one book with the most influence in their
lives; the number of books read does not affect this answer. To apply the Variance Test, try opposite answers of “1” and
a large number, say “10,000.” These numbers will not alter the evaluation of the argument, and thus this answer is
incorrect.
Answer choice (B): This is the correct answer, but it can be difficult since the wording is a bit unusual. The question is
intended to reveal how many people selected 1984 relative to the other choices, and this addresses the issue raised in
the analysis of the stimulus. Consider how the variance test works for this answer choice: First try the response, “999.”
In this case, only one person selected 1984 as the most influential book, and the argument is greatly weakened. Next
try the response, “501.” In this instance, 499 people selected 1984 as the most influential book and the conclusion is
strengthened (the other 501 people would have selected the Bible). Note that you cannot try a number larger than 501
because that would mean that the Bible was not named most often. Because the varied responses produce different
evaluations of the argument, this answer is correct.
Answer choice (C): This answer is not relevant to the columnist’s argument. Apply the Variance Test to disprove this
answer by using opposite answers of “0” and a very large number, such as “1 million.”
Answer choice (D): Because the argument is about Orwell’s 1984, other Orwell books chosen by the readers have no
impact on the argument. Apply the Variance Test, using opposite answers of “0” and a small number such as “10”
(Orwell wrote dozens of essays, but not dozens of books).
Answer choice (E): The survey in the argument addresses influence, not the actual reading of the book. A person might
be influenced by a book like the Bible through church teachings, etc. without actually having read the book. To apply
the Variance Test, try opposite answers of “0” and “1000.”
2.
The correct answer choice is (A)
Yang’s argument is as follows: Premise: Important does not mean essential. Premise: No flying machine closely
modelled on birds has worked; workable aircraft are structurally very different from birds. Premise/Sub-conclusion: So
thinking machines closely modelled on the brain are also likely to fail. Conclusion: In developing a workable thinking
machine, researchers would therefore increase their chances of success if they focus on the brain’s function and simply
ignore its physical structure.” Yang’s conclusion is very strong: “simply ignore the physical structure of the brain” when
developing a thinking machine. As you might expect, this extreme conclusion and the relatively weak supporting
evidence plays a role in the correct answer. Also note that the question stem uses the word “whether” to turn each
answer choice into a question.
Answer choice (A): This is the correct answer. The Variance Test proves the answer: If the answer is “Yes, they did
provide crucial information” then developers should not ignore the physical structure of the brain because the
reasoning used to make that judgment (via the flying machine analogy) is faulty. If the answer is “No, they did not
provide crucial information” then the argument is strengthened because the analogy suggests it would be acceptable to
ignore the physical structure of the brain. Because the varied responses produce different evaluations of the argument,
this answer is correct.
Answer choice (B): The conclusion is about ignoring the physical structure of the brain, and information about what
constitutes thinking will not help evaluate the argument. Apply the Variance Test to disprove this answer by using
opposite answers of “Yes” and “No.”
Answer choice (C): The relative amount of time spent on each project is not an issue in the stimulus. Apply the Variance
Test to disprove this answer, using opposite answers of “Yes, as much time was spent” and “No, not as much time was
spent.” Answer choice (D): The argument does not involve the background of the researchers and the projects they
work on, only what they should focus on when trying to succeed. Hence, this answer is incorrect. Apply the Variance
Test, using opposite answers of “Yes, they are among those trying to develop thinking machines” and “No, they are not
among those trying to develop thinking machines.”
Answer choice (E):The analogy in the argument is about flying machines that were modeled on birds. The possibility
that some flying machines failed that were not modeled on birds has no place in the argument. Apply the Variance Test,
using opposite answers of “Yes, some failed” and “No, none failed.”
3.
The correct answer choice is (C)
The paradox in the argument is that the provinces and states that have more stringent safety requirements also have
higher average rates of accidents. Even so, experts agree that the more stringent requirements actually are effective.
This type of “surprisingly low/high rate of success” scenario has appeared in a number of Resolve the Paradox
questions, including the following: An anti-theft device is known to reduce theft, but cars using the anti- theft device
are stolen at a higher rate than cars without the device.
Explanation: The device is placed on highly desirable cars that are prone to being stolen, and the device actually lessens
the rate at which they are stolen. A surgeon has a low success rate while operating, but the director of the hospital
claims the surgeon is the best on the staff. Explanation: The surgeon operates on the most complex and challenging
cases. A bill collector has the lowest rate of success in collecting bills, but his manager claims he is the best in the field.
Explanation: The bill collector is assigned the toughest cases to handle. These scenarios underscore the issue present in
the question: other factors in the situation make it more difficult to be successful. With the car safety requirements,
you should look for an answer that shows that there is a situation with the roads that affects the accident rates. A
second possible explanation is that the seat belts are not actually used by a majority of drivers and the safety
inspections are not made or are rubberstamp certifications. This answer is less likely to appear because it is fairly
obvious.
Answer choice (A): The stimulus specifies that annual safety inspections— regardless of what is examined—are already
in place. Therefore, this answer does not explain why the average rate of accidents is higher in those states.
Answer choice (B): Assuming that overconfidence leads to accidents, the answer could support the assertion that
states with more stringent requirements have higher accident rates. But, this answer would also suggest that the
experts are wrong in saying that more stringent standards reduce accident rates, so this answer cannot be correct.
Answer choice (C): This is the correct answer, and the answer conforms to the discussion above. If the roads are
generally more dangerous, then the stringent requirements could reduce the accident rate while at the same time the
accident rate could remain relatively high. Since this scenario allows all sides of the situation to be correct and it
explains how the situation could occur, this is the correct answer.
Answer choice (D): This answer supports only one side of the paradox. The answer confirms that the experts are
correct, but it does not explain why these provinces have higher accident rates. Thus, it does not resolve the paradox.
Answer choice (E): This answer appears attractive at first, but the number of miles of roadway in the provinces is
irrelevant because the stimulus specifically references “accidents per kilometer driven.” Since the accident rate is
calculated as per-miles driven, the actual number of miles of roadway is irrelevant.
4.
The correct answer choice is (B)
The paradox in this problem is that alcohol drinkers who surpass the threshold for calorie intake should gain weight, but
they do not. Most people, upon reading the stimulus, prephrase an answer involving exercise or some other way to
work off the expected weight gain. Unfortunately, a perfect match to this prephrase does not appear, and instead
students are faced with a tricky answer that preys upon this general idea while at the same time it fails to meet the
circumstances in the stimulus.
Answer choice (A): Read closely! The stimulus specifies that people who regularly drink two or three alcoholic
beverages a day thereby exceed the necessary caloric intake. This answer, which discusses individuals who avoid
exceeding the caloric intake necessary, therefore, addresses a different group of people from that in the stimulus. Since
information about a different group of people does not explain the situation, this answer is incorrect. This answer is
attractive because it uses the idea of getting rid of or avoiding calories, but it violates one of the precepts of the
stimulus. Out of scope! Remember, you must look very closely at the circumstances in the stimulus and make sure that
the answer you select matches those circumstances.
Answer choice (B): This is the correct answer. If the excess calories are dissipated as heat, then there would be no
weight gain. Hence, alcohol drinkers can consume excess calories and still not gain weight. Some students object to this
answer because the situation seems unrealistic. Can heat dissipation actually work off dozens if not hundreds of
calories? According to the question stem, yes! Remember, the question stem tells you that each answer choice should
be taken as true. Since this answer choice clearly states that the excess calories tend to be dissipated, you must accept
that as true and then analyze what effect that would have.
Answer choice (C): The stimulus discusses “people who regularly drink two or three alcoholic beverages a day and
thereby exceed the caloric intake necessary.” This answer choice addresses a different group of people than those
discussed in the stimulus. Out of scope!
Answer choice (D): The first flaw in this answer is that it simply states that individuals consuming alcohol do not gain
weight but it offers no explanation for why these people have no weight gain. The second flaw in the problem is that it
addresses the wrong group of people. The stimulus discusses people who drink two or three alcoholic beverages a day;
this answer addresses people who drink more than three alcoholic beverages a day. Out of scope!
Answer choice (E): Again, this answer discusses a different group of people than those in the stimulus. The stimulus
discusses people who exceed the necessary caloric intake; this answer addresses people who do not meet the
necessary caloric intake. Out of scope!
5.
The correct answer choice is (B).
The paradox in the stimulus is: for manufacturers who improved job safety training during the 1980s there was an
increase in the number of on-the-job accidents.
Answer choice (A): This answer does not provide an explanation for the paradox in the stimulus. Some students
eliminate this answer because it addresses the transportation industry, but information about the transportation
industry could be used to analogically explain the issue in the manufacturing industry (but, to be correct the answer
would have to offer some further relevant parallel between the two industries).
Answer choice (B): This is the correct answer. If the workforce is increasing, more accidents would be expected. Thus,
safety training could improve the safety of the work environment (as measured by average number of accidents per
worker, for example) while at the same time the number of total accidents could increase. Because this answer allows
both sides to be true and it explains the circumstance in the stimulus, this answer is correct.
Answer choice (C): This would explain an increase in accidents before job safety training, but the issue in the stimulus is
an increase after the safety training.
Answer choice (D): This answer further confuses the issue. If the fluctuation was random, that could explain how an
increase in accidents could follow safety training. By stating that the increase was not random, a possible cause of the
scenario is eliminated.
Answer choice (E): This answer shows that the level of safety was at least minimal prior to the safety training, but this
does not help explain why an increase in accidents followed the training.
6.
The correct answer choice is (A).
In rough terms, the paradox in the stimulus is that smokers of one pack of low-nicotine cigarettes have an identical
nicotine level at the end of the day as smokers of one pack of high-nicotine cigarettes. This similarity must be explained
by a similarity, not a difference.
Answer choice (A): This is the correct answer. The answer choice indicates that there is a similarity in the blood such
that the maximum amount of nicotine absorbed is identical for everyone. Because the maximum amount of nicotine
absorbed per day is equal to the nicotine in a pack of low-nicotine cigarettes, each person absorbs the amount of
nicotine equal to the low nicotine pack regardless of the type of cigarette smoked. Additional nicotine is not absorbed
into the blood of smokers of the high-nicotine brand. Since this answer explains the paradox, this is the correct answer.
Answer choice (B): Read closely! The stimulus is specifically about smokers who “smoke one pack of cigarettes per
day.” This answer discusses smoking different numbers of cigarettes and thus it fails to meet the circumstances in the
stimulus.
Answer choice (C): This answer confuses the issue because it indicates that most nicotine is absorbed into the system.
From this fact one would expect that those smoking high-nicotine cigarettes would have higher nicotine levels than
low-nicotine cigarette smokers.
Answer choice (D): The stimulus does not address the level of tar in cigarettes, nor can we make any judgment about
how tar affects nicotine levels.
Answer choice (E): This would apply to any smoker, and as this addresses an effect that occurs after smoking is
stopped, it does not help us understand why the nicotine rose to identical levels regardless of the kind of cigarette
smoked.
7.
The correct answer choice is (B).
The paradox in the stimulus is that raisins contain more iron per calorie than grapes even though the two are almost
identical in composition. But there is a difference: “some of the sugar in grapes is caramelized” as the grapes are dried
in the sun. Since this is the only stated difference between the two that could affect the calorie count (water has no
calories), you should focus on an answer that discusses this difference.
Answer choice (A): This answer essentially states that grapes are bigger than raisins, and you need several bunches to
equal a handful of raisins. The issue is not the size of the grapes or raisins!
Answer choice (B): This is the correct answer. If the iron content in the raisins and grapes is identical, but raisins have
fewer calories for counting purposes, then the iron per calorie will be higher for raisins, as highlighted by the following
example:
Details
Raisins
Grapes
Units of Iron (i)
100
100
Countable Calories(ii)
10
20
10 units
5 units
(Actual Calories – Caramelized Calories)
Iron Per Calories- (i/ii)
Note that the paradox could have addressed any common element between raisins and grapes (such as fiber or fat),
and raisins would always have the higher per calorie content since they contain fewer countable calories.
Answer choice (C): The paradox in the stimulus does not involve the rate at which the body can absorb iron or any
other nutrient. This answer misses the point and is incorrect.
Answer choice (D): The availability of raisins and grapes is not an issue in the stimulus. The answer then discusses iron,
but the point made about yearly intake is irrelevant.
Answer choice (E): The comparison in the stimulus is between grapes and raisins. This answer, which brings in other
food items, is irrelevant.
8.
The correct answer choice is (D).
The situation in the stimulus is that vervet monkeys use different calls depending on where predators come from. The
correct answer must explain why the calls are different (again, difference versus similarity is an issue). Note that the
stimulus does not contain a true paradox, just an odd situation that is presented without explanation.
Answer choice (A): This answer states that vervet monkeys vary the calls in order to indicate the number of predators,
but the answer does not explain why different calls are used for land versus air predators. This answer is attractive
because it shows that different calls can be used to indicate different things, but it is wrong because it does not explain
the behavior of the monkeys as described in the stimulus.
Answer choice (B): This answer addresses only land-based predators and does not explain the difference described in
the stimulus.
Answer choice (C): This answer states that the predators using land attacks are different from the predators using air
attacks, but this information does not explain why vervet monkeys use different calls to indicate that fact.
Answer choice (D): This is the correct answer. Because vervet monkeys react to predators in different ways, they would
need to know if the predator was coming by land or air. Hence, the different calls are used to tell the monkeys whether
they should climb trees or dive into the foliage. Since this answer explains the behavior of vervet monkeys, this answer
is correct.
Answer choice (E): The diet of selected predators of vervet monkeys is irrelevant and does not help explain why vervet
monkeys use different calls depending on the direction of the attack.
Critical Reasoning
Tips & Strategies
Here are Manhattan Review’s five top strategies for attacking Sentence Correction questions:
1.
2.
3.
4.
5.
Don’t expect the right answer to read like a sentence crafted by Henry James or Gustave Flaubert. The best sentence is
often the best of a bad bunch—it’s the one with the least number of egregious errors. Therefore, don’t be put off if the
sentence you choose sounds awkward. If the worst thing about it is that it sounds like something your boss might dash
off in an office memo, don’t worry.
More than half of the Sentence Correction exercises will involve at least one Subject-Verb agreement issue. Therefore,
always make sure you’ve got all of your ducks in a row and that all of the subjects are properly aligned with their verbs.
Remember, a subject has to agree with a verb, as a matter of number and as a matter of logic.
Make sure your pronouns are lined up properly with their antecedents. If the antecedent is plural, the pronoun
replacing it must be plural. This is a particularly important issue in long, convoluted sentences in which it is easy to
forget a pronoun’s antecedent.
Get your comparatives sorted out. “As” goes with “as”; “more,” “less” and “fewer” go with “than.” Never combine the
two. Sentences such as “The girls fared as well or better than the boys.” It has to be one or the other: “The girls fared as
well as the boys.” Or “The girls fared better than the boys.”
Make life easy for yourself and narrow your choices down as quickly as possible. Spot the critical issue and eliminate
the answer choices that obviously come down on the wrong side of it.
Take a look at the following sentence from Manhattan Review’s course material as an example:
Many companies pay almost twice as much to men, if the effect of faster promotions, more bonuses, and better benefits are
regarded as salary, than to women, who earn 77 cents for every dollar their male counterparts earn in base salary.
A.
B.
C.
D.
E.
are regarded as salary, than
are regarded as salary, as
is regarded as salary, than it pays
is regarded as salary, as is paid
is regarded as salary, as they pay
Well, as you will agree, the sentence sounds awkward. So the first point is satisfied. The non-underlined or supposedly OK part
of the sentence includes the words “if the effect of.” They introduce a lengthy intervening phrase. Coming just after the words
“as much to men,” this phrase adds confusion. The word “if” is being used to condition a statement—a statement that has not
yet been made. We don’t yet know what exactly companies are doing to men but already we are told about the “effect” that
something or other will have.
The second point is also in play here. Underlined is the verb “are.” The word is just dangling there and we have to figure out the
subject that goes with it. Since the words “faster promotions, more bonuses, and better benefits” lie next to it, it seems at first
glance as if they constitute the verb’s subject. However, on closer examination, it is apparent that “faster promotions and so on”
can’t be regarded as salary. That makes no sense. No, it is the “effect of” faster promotions and the rest that is the subject of the
verb.
That makes life nice for us. The words “effect of” are not underlined. That means it is a singular subject. And a singular subject
must go together with a singular form of the verb. Therefore, the word “are” cannot be correct here. That means we can
eliminate answer choices (A) and (B). Point No. 5 has come into play.
Answer choice (C) can also be eliminated. The pronoun “it” clearly has as its antecedent the noun “many companies.” A plural
subject can only be replaced by a plural pronoun. That’s the issue Point 3 was addressing. As if that were not bad enough (C) has
the comparative “as” going together with “than.” That’s unacceptable. You can have “Companies can pay men twice as much as
they pay women” or “Companies pay men more than they pay women” or “Companies pay men more than twice as much as
they pay women.” But you can’t have “Companies pay men twice as much than women.” That’s Point 4.
(D) is also out. “As” requires parallelism. It is a comparative. We are comparing what companies pay men with what companies
pay women. But (D) is comparing what companies pay men with what women are paid. What companies do is being compared
to what women make. The parallelism is faulty.
By a process of elimination, we are left with (E). Subject and verb are aligned, the pronoun refers to the right antecedent and
our comparatives are parallel and in synch. So this is the best answer.
Best of luck on your MBMAT test day!
9.
Answer – B– Run-on, Parallelism, Verb
The sentence as given is a run-on sentence because it uses a comma to connect two independent clauses. B is the best
answer as it gets the placement of ‘both’ right and also uses the parallel structure correctly.
C - The placement of ‘both’ is incorrect. The original sentence implies that the release of Jurassic Park led to the
inauguration of two things; hence ‘both’ should come after ‘inauguration’
D - The use of ‘and’ is not appropriate since it fails to show the causal relationship implicit in the sentence. Also the
preposition ‘of’ does not have to be repeated in the phrase ‘of the audience’s fascination with dinosaurs’ because ‘of’ is
coming before ‘both, which implies that it applies to both the things that come after ‘both’.
E - This sentence is missing a main verb
10. Answer – A– Meaning (Modification), Idiom
The sentence starts with a modifying phrase - Indicating their desire to rid the country of corruption, - so what follows
should be whoever is indicating this desire. Since the pronoun used in the modifying phrase is the plural ‘their’, the
subject also has to be plural i.e. it can’t be the leader of the ‘Banish Corruption’ party. Hence eliminate B, C, and E.
Both A and D are grammatically correct but D gets the meaning upside down by suggesting that the President was
elected as the leader whereas it was actually the leader who was elected as the President. Also D gets the idiom wrong
– the correct idiom is ‘elected as’. Hence A is the best answer.
11. Answer– C– Parallelism, Meaning, Run-on
C gets the parallelism right (‘praise’ and ‘show’) and is the best answer.
A - Breaks the parallelism by using ‘it’. Also it’s not clear who is the subject in the second clause after the comma
B - The use of ‘rare’ as an adjective to modify ‘kindness’ distorts the meaning of the original sentence by suggesting that
the academicians are actually showing a type of kindness (rare kindness) towards contrary theories.
D - This is a run on sentence because a comma is used to connect two independent clauses
E - Same as B
12. Answer – D– Wordiness, Pronoun reference
The relative pronoun ‘that’ cannot be used to modify living things such as ‘painter’, hence A is incorrect.
C goes out because the ‘it’ at the end of the sentence has no antecedent.
E is unnecessarily wordy.
Between B and D, ‘is able to make’ is the same thing as ‘makes’, so B is unnecessarily wordy and D is the best answer.
13. Answer – C– Redundancy, Meaning,
The use of ‘because’ and ‘is the reason’ in the same sentence is redundant, so eliminate A. C gets this right and is the
best answer.
B - This sentence makes it appear as though ‘lack of education’ is the reason why planners attack illiteracy first,
whereas it is the entire first clause that is the reason and just the lack of education
D - Awkward and wordy construction because of the usage of ‘being’.
E - Distorts the meaning by changing ‘social ills’ into ‘illnesses in society’
14. Answer– B– Sub-verb Agreement, Pronoun reference
This sentence is testing you on the knowledge of singular and plural. Remember that we have a compound subject accounting and cost-management - so the verb needs to be plural as well. B is the best answer.
A - Two things can be ‘examples’ and not ‘an example’.
C - The singular ‘financial field’ does not agree with the compound subject
D - The singular ‘financial field’ does not agree with the compound subject
E - The pronoun ‘they’ has no logical referent
15. Answer– D– Run-on, Verb Tense, Meaning
The sentence as given is a run-on because it uses a comma to connect two independent clauses. D corrects this by using
a semi colon between the two clauses.
B – Gets the tense wrong – we require the past tense ‘set’ and not the present tense ‘sets’
C - This is again a run-on sentence
E - Incorrectly uses ‘by’ to show a causal relationship between the first and the last parts of the sentence
16. Answer– E– Modification
Here the word "Impressive" modifies the word "number". The word that modifies impressive should be Increasingly. So
we can clearly eliminate A and C.
Increasing is an adjective- which gives us the wrong meaning when we read. And Increasingly is an adverb, gives us the
correct meaning while reading the sentence. B is awkward- "those not yet born" we would rather prefer simple
"unborn" instead of that. So eliminate B. Same with the D. "all of them" is awkward and redundant. since we have "the
unborn"- Noun The answer should be E.
Reading Comprehension
17.
18.
19.
20.
D
E
B
D
Quantitative Section
Maths Section
1.
Answer: E.
xy + z = x(y + z)
xy + z = xy + xz
So, xy cancels out
xz - z = 0
z(x-1) = 0
either z = 0 (in this case x can take ANY value) OR x = 1 (in this case z can take ANY value).
To elaborate more: As the expression with y cancels out, we can say that given expression xy + z=x(y + z) does not
depend on value of y. Which means that y can take ANY value. So all answer choices which specify the exact value of y
are wrong.
NOTE: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER
value must be true.
Answer E
2.
Answer B
Given: 0.7b + 0.5a = 6.3 Question: a + b=?
0.7a + 0.5b = 6.3
7a + 5b = 63.
After some trial and error you'll get that only two integer pairs of (a, b) satisfy this equation: (9, 0) and (4, 7) as we are
told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: a = 4 and b = 7 so,
a + b=11.
Answer: B.
3.
Answer C
When trying the first time the probability Sarita doesn't pick the correct combination = 3999/4000 Second time, as the
total number of possible combinations reduced by one, not picking the right one would be 3998/3999.
Third time 3997/3998 ... …
And the same 75 times.
So we get: 3999/4000*3998/3999*...*3925/3926 every denominator but the first will cancel out and every nominator
but the last will cancel out as well.
If Sarita does not pick the correct combination in first 75 try, then the correct combination is one of remaining 3925. So
Probability = 3925/4000 = 157/160.
Answer: C.
4.
Answer B
In the right triangle
We know,
Sin 30
Or,
height/hypotenuse
Since,
hypotenuse, PQ
Height/4
Or,
height
Therefore, area
Answer: B
5.
= 1/2
= 1/2
= 4,
=1/2
=2
= base * height = 2*6=12
Answer E
Do not overcomplicate - they ask for the number of people who did not answer "yes" to BOTH questions, while you are
calculating "not yes for ANY of the 2 questions".
Those who answered yes to both questions = 1/4 x 1/3 = 1/12
So those who did NOT answer "yes" to both questions? = 1 - 1/12 = 11/12
Answer E
6. Answer B
B speed: 2 mph;
A speed: 3 mph (travelling in the opposite direction);
r = 10 miles
Track distance: 2*π*r=20* π;
What distance will be covered by B in 10 hours at 2 mph: 10*2=20 miles
Distance between B and A by the time, A starts to travel: 20*π – 20
Time needed for A and B to meet distance between them divided by the relative speed:
=
(as they are travelling in opposite directions relative speed would be the sum of their rates (2+3);
=
=4*π - 4
Time needed for A to be 12 miles ahead of B:
= 2.4;
So we have three periods of times:
Time before A started travelling: 10 hours;
Time for A and B to meet: 4*π - 4 hours;
Time needed for A to be 12 miles ahead of B: 2.4 hours;
Total time: 10 + 4*π – 4 + 2.4 = 4*π + 8.4 hours.
Answer B
7.
Answer B
Given:
Average of 20 numbers
=
Or,
=
Or sum of 20 numbers
So, sum of 21 numbers
= 5n
= sum of 20 numbers + n
= 5n + n
= 6n;
Now the question: n is what fraction of the sum of the 21 numbers in the list?
=
= 1/6
Answer B
8.
9.
Answer is B
Initially take X for total laptop owners and Y for Total cell phone owners.
Then solve for total people without laptops =.6X (laptop owners[X]-without laptop [W/O L] = 40% of laptop owners[X])
Then the net total becomes X+.6X=1.6X.
Solve for Y under cell phone column i.e. Y = .3Y + .56X resulting in Y = .8X and that’s it.
In the end you get the value under "neither cell phone nor laptop column" = .36X.
And (.36X/1.6X)*100 = 22.5%
Answer B
Cellphone
Without Cellphone
Total
Laptop
.56X
.44X
X (with laptop)
Without Laptop
.30Y
.36Y
.6X (without laptop)
Total
Y
1.6X - Y
1.6 X
X- w/o laptop = .4X
so, without laptop = .6X
Answer A
What combinations of two cards are possible to total 8?
(First card, Second card):
(6, 2)
(2, 6)
(5, 3)
(3, 5)
(4, 4)
Only 5 possible scenarios for total sum to be 8. One from this 5 has already happened. Notice here that the case of (6,
2) is different from (2, 6), and similarly the case of (5, 3) is different from (3, 5).
From these five cases, only in two we have 5. So, the probability is 2 chances out of 5 that the one that occurred had 5:
P=2/5.
Answer: A.
10. Answer B
Since, 200 students answered "yes" only for subject M. Then, the remaining 300 students who answered "yes" for
subject M, also answered "yes" for subject R.
So, 300 students answered "yes" for both subjects.
If 300 students answered "yes" for both subjects,
Then, 400 - 300 = 100 students answered "yes" only for subject R.
So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;
Therefore 800-(200+100+300) = 200 students did not answer "yes" for either subject.
Answer: B.
Data Sufficiency
11. Answer A
Question Type: What Is the Value? This question asks for the specific value of x – y. Given information in the question:
No important information is given in the question. Note that you only need to find the difference between the two
variables. This will usually require less information than solving for the individual variables.
Statement 1: This is a perfect example of using algebraic manipulation to find the value of x – y. By digging deep into
your algebra toolkit and by using your understanding of the common algebraic equations, you should manipulate
2
2
2
accordingly: (x + y) = 4xy can be rephrased as x + 2xy + y = 4xy. Subtract 4xy from both sides to create the quadratic
2
2
equation x – 2xy + y = 0. This can be factored to (x –y) (x – y) = 0. Therefore x – y = 0. This statement is sufficient, and
the answer is either A or D.
2
2
Statement 2: x – y = 0. This statement again requires proper algebraic manipulation and recognition of the difference
2
2
of squares: x – y = 0 is the same as (x +y) (x –y) = 0. However, it is not clear whether x + y = 0 or x – y = 0 so this
statement is not sufficient.
The correct answer is A. Note: This problem demonstrates how important it is to have a high level of fluency in algebra,
and with the common algebraic equations in particular. There is no way to prove sufficiency here without this fluency.
12. Answer B
Question type: Yes/No. The question asks: “Is the product (a) (a + 1) (a +2) divisible by 48?” You can think ahead of time
that in order to be divisible by 48 this product must have the prime factors of 48: 24 • 3. So the question is really: Does
this product contain at least four 2s and one 3? Given information in the question: “a is a positive integer.” Since a is a
positive integer the rule that “in any three consecutive integers one of those integers will be a multiple of 3” applies.
That means that before you even go to the statements you know that the product (a) (a + 1) (a +2) will be a multiple of
3. The question then can be simplified even more from above because you know that the factor of 3 will be present.
The simplified question is: Does this product have 24 as a factor? It is essential that you always leverage all given
information in the question before moving to statements. Also note that this problem (as is true for most arithmetic
problems) is best solved with your conceptual understanding of factors and divisibility. While you could prove
sufficiency/insufficiency with number picking, it would be cumbersome and risky in this example.
Statement 1: a is even. If a is an even number, it means that a will contain at least one 2 as a factor. It also means that a
+ 2 will be even and that one of those two even numbers will be a multiple of 4. For example, if x = 2 then (x +2) = 4.
This means that you have at least 23 as a factor. However, this statement is not sufficient as it only guarantees three 2s
in the product and not the required four 2s. Eliminate choices A and D.
Statement 2: If 4a is divisible by 32 then “a” must be divisible by 8. If a contains three 2’s as factors then this
information is sufficient as you know that (a + 2) will have to contain at least one 2 as well. This statement is sufficient
to prove that the product will contain 24 • 3 and the correct answer is B.
13. Answer A
Question Type: What Is the Value? This question asks for the area of the rectangle PQRS.
Given information in the question diagram: The diagram is given and importantly one side is defined with PS = 4, so
both PS and QR = 4. To find the area you need to somehow determine either RS or PQ from the information in the
statements. The question is really: What is RS or PQ?
Statement 1: QTR is an equilateral triangle. If this is true, then with QR as the base, the height of the equilateral triangle
is equivalent to the side that you are trying to determine (PQ or RS). Since the base of QTR is 4 you can determine the
necessary height with your knowledge of 30–60–90 triangles or simply with your knowledge that if you know one thing
about an equilateral triangle, then you know everything! While you do not need to calculate it, the height would be
2√—3 as it is the long leg in a 30–60–90 triangle formed by 12 the base of QTR (2), the hypotenuse QT (4) and the
height ( 2√3 ) which is equivalent to PQ or RS. Statement 1 is sufficient, so the answer is A or D.
Statement 2: In this difficult statement, the testmakers are playing with a common trick. They have polluted your brain
with the first statement and want you to assume that if “segments PT and TS have equal lengths,” then QTR must again
be equilateral. However, this statement does nothing to help you determine the length of the sides (QP and RS)
because it only proves that QTR is isosceles. There is no limit put on the lengths of PQ and RS (because you do not know
the angle of TQR and TRQ) with this statement, so it is not sufficient. Remember: One of the keys to success in Data
Sufficiency is to consciously avoid assumptions, but that can be hard when you are set up so nicely to make
assumptions with the other statement. Statement 2 is not sufficient, so the correct answer is A.
14. Answer A
Question Type: Yes/No. The question asks: “Is 1/x + 1/y = 16?”
Given information in the question stem or diagram: xy does not equal 0. This is important only because x and y cannot
be 0, as they are denominators. Importantly, you should manipulate the equation in question. As you learned with the
Algebra Toolkit, in almost any equation involving fractions, the first step to simplification is to remove the
denominators. Here that is done by multiplying the equation by xy to create the new question: Is y + x = 16xy?
Statement 1: If you have done the proper manipulation as shown above, it is clear that this statement is exactly the
same as the changed question and thus sufficient. The answer is A or D.
Note: Do not forget that on many harder Data Sufficiency questions it is easier to change the question to match the
statements than vice versa. This provides an excellent example of this phenomenon and shows the importance of
proper algebraic simplification in Data Sufficiency questions.
Statement 2: If you take this information (x = y) and substitute it into the question above you get: Is 2x = 16x2? Or: Is 2y
= 16y2? These questions are impossible to answer, as you do not know anything about the value of x or y. Statement 2
is not sufficient so the answer is A.
Note: If you picked answer C on this question you have fallen for the “C Trap”! Most test-takers immediately see that
this question can be answered with both statements together, as substituting x for y turns Statement 1 into a single
variable equation, allowing you to solve for one variable, which we know from Statement 2 is exactly the same as the
other. But in situations in which C seems “too easy,” one should take the more-comprehensive statement and try to
exhaust it, as the MBMAT is apt to reward you for being able to obtain more value from each resource. Statement 1, as
shown earlier, is actually the same as the question, but this is only apparent after the proper manipulation shown
above.
15. Answer E
Question Type: What Is the Value? This is a Venn Diagram question and the question asks: “How many students take
both French and Spanish?”
Given information in the question stem: In any Venn Diagram problem you should draw out the diagram and remember
that Total = Set 1 + Set 2 – Both + Neither. It is important to always consider “Neither” in these types of DS questions
and to note the difference between total set information and “only” information (for instance, the difference between
people who take “only French” and “French”).
Statement 1: French = 100 and Spanish = 125. This can be written to say that French + Spanish – Both + Neither = Total
or 100 + 125 – Both + Neither = Total. This statement is not sufficient alone because you do not know how many total
students there are, nor how many students take neither French nor Spanish. Not sufficient. Eliminate choices A and D.
Statement 2: Total students = 200. This is not sufficient alone since there is no way to allocate the 200 students among
the categories. Eliminate choice B.
Together: Many students will think that the answer is C because they have forgotten to consider “Neither.” You do not
know how many students take neither French nor Spanish, so there is no way to determine “Both.” Without this
information you only know that at least 25 students take BOTH (that is if Neither = 0) and as many as 100 might take
BOTH if the neither category was 75. This is not sufficient and the correct answer is E. Note: In any choice between C
and E such as this you must learn to Play Devil’s Advocate and consider anything you might be missing. In this example
(as with many Venn problems) that is making sure you remember to consider the value of “Neither.”
16. Answer B
Question Type: Yes/No. The question asks: “Is x positive?”
Given information in the question stem: No important information is given in the question stem.
2
Statement 1: x = 9x. Many students will think that x = 9 after dividing both sides by x and thus believe that this
statement is sufficient. However, it is important to consider all of the possibilities, and you are not allowed to divide by
2
x if it is 0. Given this, the best way to approach this question is to subtract 9x from both sides to get x – 9x = 0. Factor
out x and see that: x(x – 9) = 0. So clearly x can equal 9 or 0. Because this is a yes or no question, you must check each
value to get a “yes” or a “no.” Just because you have two values for x does not make the statement automatically
insufficient. x = 9 gives you a “yes” since x is positive. x = 0 gives you a “no” since zero is not greater than zero. So this
statement is not sufficient and the answer is either B, C, or E. Note: This is a common and tricky algebraic set-up in data
sufficiency. Mathematically, whenever you have a squared variable you should set the equation equal to zero and
factor.
Statement 2: | x | = -x. This statement appears more difficult than it really is. The key of course is to figure out what
this equation tells you about x. Hopefully you recognize that x must be negative OR zero given this statement, but if
not, you can try some numbers to prove it. Try a positive number for x such as 9. That gives you | 9 | = -9, which means
“9 = -9.” This is not true so you can see that any positive numbers are excluded by this statement. Try a negative
number: x = -5. Now |-5 | = -(-5), which means 5 = 5. This is true so you can see that this statement allows for negative
numbers. You will also want to try zero, but as in the last statement, many students forget about zero. | 0 | = -0. This is
true (0 = 0) so negative numbers as well as 0 work for this statement. Taking these back to the question you see that
any negative numbers give you a “no” answer. Zero also gives you a “no” answer so there is a consistent “no” and this
statement is sufficient. The answer is B.
Note: The difficulty of this question lies in both the tricky algebra and in the fact that you might pick answer C even if
you do the algebra properly. Why? Because people forget that “no” is just as good as “yes” in the second statement
and they also see that 0 nicely overlaps between the statements, making it tempting to think “C.” If the question was
asking “What is the value of x?” then the answer would be C. However, since this is a Yes/No question, the second
statement gives you a definitive answer and is thus sufficient.
17. Answer A
Question Type: What Is the Value? This question asks for the average of the terms in set J.
Given information in the question stem: No important information is given in the question stem.
Statement 1: The sum of any three terms in the set is 21. This is a very difficult statement to consider. Clearly this WILL
be true if all the terms are 7, but you need to make sure there are not any other possibilities. Will it work with any other
sets, such as “6, 7, 8, 6, 7, 8”? Adding certain numbers in this set will give you 21, but not “any three terms.” The only
ways to ensure that any three randomly chosen terms will sum to 21 are either to have only three terms (say, 6 + 7 + 8)
or to have all terms in the set equal 7. In either case, the average must be 7, so this is sufficient information. The
answer is A or D.
Statement 2: Set J consists of 12 terms. This statement is not sufficient on its own since it does not give any values for
the terms in the set. However, as is the case with any clearly insufficient statement such as this, you must consider
whether it is important with the other statement. This statement was clearly designed to make choice C a more
attractive option, but you do not need to know anything about the number of terms for the first statement to be
sufficient. The correct answer is A.
18. Answer B
Question Type: Yes/No. The question asks whether line M runs through point (6, 6).
Given information in the question stem or diagram: Line M is tangent to a circle; the circle is centered on point (3, 4).
Statement 1: Line M runs through point (-8, 6). This statement is not sufficient because there is no information about
the size of the circle or the direction that line M is running. Simply having a single point on line M will not be sufficient
to answer the question. Eliminate choices A and D.
Statement 2: Line M is tangent to the circle at point (3, 6). Many people will immediately combine this with Statement
1 in their minds and think that with both statements you know that M is the straight line y = 6, in which case line M
would definitely run through point (6, 6). However, before you jump to this stage, remember that you only get to
combine statements when neither statement is sufficient alone. Before you pick choice C in a question like this, it is
always essential that you take a closer look at each statement individually.
The definition of tangent is very important for Statement 2 and it is what differentiates Statement 2 from Statement 1.
A line that is tangent to a circle touches that circle in only one place and is perpendicular to that circle at that point.
Given that the center of the circle is at (3, 4) and the point of tangency is at (3, 6), you can conclude that line M is
perpendicular to the line x = 3. Therefore line M must be the line y = 6, and it does pass through (6, 6). This statement is
sufficient alone and the answer is B. Note: This is another great example of the “C trap” set-up in which test makers
give you two statements that fit together nicely but are not both required to answer the question. To combat this setup, use the reward system from the lesson and always double-check each statement alone before picking answer C.
19. Answer A
Question Type: What Is the Value? The question asks you for the remainder when x is divided by 10.
Given information in the question stem: x is a positive integer. When x is divided by 7 the quotient is q and the
remainder is 1. Number picking is an important and valid strategy in quotient/remainder questions, so you might even
want to consider possibilities for x before moving to the statements. If the remainder is 1 when x is divided by 7, then x
could be 1, 8, 15, 22, 29, 36, 43, etc., yielding different quotients for q.
Statement 1: When x is divided by 5 the quotient is q and the remainder is 1. In the question stem, you learned that
when x is divided by 7 the quotient is also q and the remainder is also 1. Most students understand that if you divide x
by two different divisors and get the same remainder, x must equal the sum of the remainder and a multiple of the
divisors’ LCM. For instance, if you divide a number by 5 and 7 and get a remainder of 1, then that can happen at 35 + 1;
70 + 1; 105 + 1; etc. 276
However, if you read carefully you see that the quotient is the same in both operations, a puzzling result. Clearly if you
divide 36 by 7 it will give you a different quotient then when you divide 36 by 5. However, students will overlook this
important fact (that q is the same in both cases) and believe that there are multiple possibilities for x and thus multiple
possibilities for the remainder when you divide x by 10. The only way you can have the same quotient and the same
remainder when you divide by two different numbers is if you are dividing a smaller number by a bigger number—in
this case 1. Remember that when a smaller integer is divided by a larger integer, the quotient is always 0 and the
remainder is the dividend itself. Here when 1 is divided by 7 the quotient is 0 and the remainder is 1, and when 1 is
divided by 5 the quotient is also 0 and the remainder is 1. Statement 1 is sufficient, as x must be 1 and the remainder
when x is divided by 10 is also 1. The answer is either A or D.
Statement 2: x is less than 50. This is clearly not sufficient by itself. This statement is here for people who miss that the
quotient is the same and think that x could be any (multiple of 35) + 1. By knowing that x is less than 50 it would seem
to lock in the value at 36. However, from the discussion above it is clear that this would be incorrect. This is a very
clever “C trap” because it makes the person choosing answer C feel like they have understood the problem while the
answer is really A. The only way to get this right is by knowing this tricky and easily overlooked fact in Arithmetic and by
reading the information closely (leveraging that q is the same when dividing by two different numbers—a puzzling
result).
20. Answer A
Question Type: What Is the Value? This question asks you for the specific value of
Given information in the question stem or diagram: a, b, and c are integers, and
= 1. Before going to the
statements it might be helpful to restate that equation. If you multiply both sides by b – c, the equation becomes a = b
– c. Looking back to the question you can now phrase the question as “What is
?” Remember that often the
important work in Data Sufficiency questions relates to manipulating the information in the question stem, not just in
the statements.
Statement 1: “
question:
= 35 .” The work that you did on the question has paid off. This statement exactly answers the
= 35 . This is sufficient, and the answer is either A or D.
Statement 2: “a and b have no common factors greater than one.” This means that a and b are what is called “coprime.” For example, 8 and 9 are “co-prime.” Neither has to be a prime number but in relation to each other they have
no common factors greater than 1. This statement is not sufficient, as there are many co-prime numbers. Since this is
clearly insufficient by itself, it is a “Why Are You Here?” set-up and you should wonder why test makers are delivering
this statement. Is it important? It would be important if you were trying to find the value of a or b individually, but since
the question only asks for a ratio, the individual values of a and b are not important and the answer is A.
ESSAY SECTION
Tips and Strategies
In this Analysis of An Issue section, an issue will be presented and you will be asked to analyze it and explain your views
on it together with examples from your own experience, observations or reading.
These ISSUES themselves fall into two categories
I.
One in which two opposite views on an issue are presented and you are asked to take a position in
favour of one of them and defend that position.
II.
One in which only one view is presented and you are asked whether you agree or disagree with it and
called upon to defend your position.
How You should start:
Do not start scribbling on the answer sheet with your pencil immediately on seeing the question.
Take a few minutes to think about the issue and plan a response before you begin writing. Be sure to organize your
ideas and develop them fully, but leave time to reread your response and make any revisions that you think are
necessary.
The 20 minutes you are allowed to write the essay is not a long time and no one is capable of writing a profound,
thoroughly developed, well-crafted and technically perfect essay in just 20 mins.
And your essay need not have all these qualities to earn you a high score.
The opinion in an Analysis of An Issue essay is stated in such broad and general terms that almost anyone can find
something to say either in favour or against it.
 The first step in developing your essay is to brainstorm ideas about what to say. There is no pre-set or magic
formula for this process. You should first take about two minutes to understand the issue and think of points
both in favour and against what is stated.
 Then jot down on a scrap sheet these points on either side of a centre line. You will probably find that you
have more points on one side than on the other. Adopt the side on which you have more points as your
opinion.
 Remember that there is no right or wrong opinion which decides the score that you will be awarded. What’s
needed is that you should write a cogent and logical essay supporting your opinion.
 Then look at your notes and pick the three or four ideas you like best. These should be ideas which you think
make sense, relate to the topic and support your point of view reasonably well.
 Put a check mark next to those ideas so that you spot them easily when you start composing your essay.
Finally, decide on the sequence for the ideas. This can be done in several ways. Often the sequence will be
obvious. One idea may be the fountainhead of all others and therefore should clearly come first. Sometimes
the ideas may all reflect historic events that took place in a definite time sequence. If there is such an obvious
sequence, use it.
 The most emphatic parts of any essay the parts that the reader is most likely to remember or be impressed
with - are the beginning and the end.
How Your Analysis of An Issue should be:




Begin the essay with a brief introductory paragraph that sets forth your point of view clearly and, if you like,
also suggests the nature of the ideas you will be using to defend it. The side you are proposing to take on the
issue should be brought out clearly in the first paragraph itself.
Have three or four middle paragraphs to substantiate your view with examples or illustrations.
End the essay with a brief concluding paragraph which summarizes your point of view in a clear, concise and
forceful way.
The last step in the process is a quick revision of your essay to eliminate inadvertent errors in spelling and
grammar that you might have committed.
Evaluation of Your Response
College and university faculty members from various subject matter areas, including management education, will
evaluate the overall quality of your thinking and writing. They will consider how well you—organize, develop, and
express your ideas about the issue presented provide relevant supporting reasons and examples and control the
elements of standard written English.
ANSWER TO ESSAY SECTION
1.
Are professional success and a fulfilling personal life mutually exclusive? Probably it is not so, although it is more
difficult today to achieve both.
Undeniably, today's professionals must work long hours to keep their heads above water, let alone to get ahead in
life financially. This is especially true in Japan where cost of living coupled with corporate culture compels
professional males to all but abandon their families and literally to work themselves to death. While the situation in
other countries may not be as critical, the two-income family is now the norm, not by choice but by necessity.
However, our society's professionals are taking steps to remedy the problem. First, they are inventing ways-such as
job sharing and telecommuting-to ensure that personal life does not take a back seat to career. Second, they are
setting priorities and living those hours outside the workplace to their fullest. In fact, professional success usually
requires the same time-management skills that are useful to find time for family, hobbies and recreation. One need
only look at the recent American presidents-Clinton, Bush, Reagan, Carter and Obama- to see that it is possible to
lead a balanced life which includes time for family, hobbies and recreation while immersed in a busy and successful
career. Third, more professionals are changing careers to ones which allow for some degree of personal fulfillment
and self- actualization. Besides, many professionals truly love their work and would do it without compensation, as
a hobby. For them, professional and personal fulfillments are one and the same.
In conclusion, given the growing demands of career on today's professionals, a fulfilling personal life remains
possible by working smarter, by setting priorities and by making suitable career choices
CASE ANALYSIS
There is no perfect answer for a case analysis problem. So we cannot provide you with the best fit answer. All
answers will be evaluated individually as per its content and effectiveness in addressing the issues in the given
case.
Best of Luck