PATH (ENGGINEERING)
PACE APTITUDE & TALENT HUNT
(QUESTION PAPER)
1.
Three years ago, the average age of a family of 5 members was 17. A baby having been born, the
average age of the family is the same today. The age of the child is
(A) 3 years
(B) 4 years
(C) 2 years
(D) 1 year
2.
When the price of gold went up, a jeweler raised the price on certain rings by 60%. On one ring
however, the price was accidentally reduced by 60%. By what percent must the incorrect price be
increased to reflect the proper new price?
(A) 300%
(B) 500/3%
(C) 400%
(D) 120%
3.
Sameer drove to a place at 60 km/hr. Returning over the same route, due to traffic, he could drive at
40 km/hr. If the return trip took one hour longer, how much distance (in kms.) did he drive each
way?
(A) 2
(B) 3
(C) 120
(D) 240
4.
If, in the adjoining figures, the area of rectangle ABCD is 100, what is the area of rectangle PQRS?
A
x+ 4
B
P
x+ 1
C
D
(A) 105
(B) 104
x+ 3
Q
x+ 2
S
R
(C) 102
(D) 101
5.
In a right triangle, 1/4 of the length of the longer leg is equal to 3/5 of the shorter leg. What is the
ratio of the length of the hypotenuse to the length of the shorter leg?
(A) 13 : 5
(B) 12 : 5
(C) 13 : 9
(D) 13 : 4
6.
From 2002 to 2003, the sales of a book decreased by 80%. If the sales of 2004 were the same as in
2002, by what percent did they increase from 2003 to 2004?
(A) 20%
(B) 80%
(C) 120%
(D) 400%
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7.
A man on the deck of a ship is 16 m above water level. He observed that the angle of elevation of the
top of a cliff is 45° and the angle of depression of the base is 30° . What is the height of the cliff?
(A) 43.712
(B) 44.631
(C) 45.236
(D) 42.146
8.
Two motorist met at 10 am at Dadar railway station. After meeting, one of them proceeded in the
east direction while the other proceeded in the North direction. Exactly at noon, they were 60 km
apart, find the speed of the slower motorist if the difference of their speed is 6km h .
(A) 28km h
(B) 18 km h
(C) 9km h
(D) 19km h
9.
A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much
time would it take the monkey to reach the top?
(A) 18
(B) 19
(C) 20
(D) 21
10.
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180 . The
original price of petrol will be(A) 5$ per gallon
(B) 6$ per gallon
(C) 4$ per gallon
(D) 8$ per gallon
11.
A shopkeeper sells two items at the same price. If he sells one of them at a profit of 10% and the
other at a loss of 10% , then the percentage profit/ loss will be(A) 2% loss
(B) 3% profit
(C) 1% loss
(D) 2% profit
12.
Dolly goes to a shop to purchase a doll priced at Rs 400 . She is offered 4 discount options by the
shopkeeper. Which of these options should be the option to gain maximum advantage of the discount
offered?
(B) 2 successive discounts of 15% each
(A) single discount of 30%
(C) 2 successive discounts of 20% & 10% (D) 2 successive discounts of 20% &12%
13.
There is a point inside an equilateral triangle which is at distances 1, 2 and 3 from the three sides.
The area of the triangle is:
(A) not uniquely determinable
(B) 6
(C) 6 3
(D) 12 3
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14.
If x5 + kx2 is divided by (x – 1) (x – 2) (x – 3), the remainder contains no terms in x2 then k =
(A) 90
(B) 100
(C) – 90
(D) – 70
15.
If x+௫ = 2, then ‫ ଼ ݔ‬+ ௫ ఴ is equal to:
ଵ
(A) 1
ଵ
(B) 3
(C) 2
(D)
2
16.
In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came
to the town with certain number of flowers. Before entering the first temple, he washed all the
flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to
the God in the first temple and moved to the second temple. Here also, before entering the temple he
washed the remaining flowers with the water of well. And again his flowers doubled. He offered few
flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled
after washing them with water. He offered few flowers to the God in third temple. There were no
flowers left when pilgrim came out of third temple and he offered same number of flowers to the
God in all three temples. What is the minimum number of flowers the pilgrim can have initially and
how many flower did he offer to each God?
(A) 21 & 24
(B) 28 & 25
(C) 14 & 15
(D) 7 & 8
17.
The mean of n observations is x . If the first observation is increased by 1, the second by 2, the third
by 3, and so on, then the new mean is
n +1
n +1
(A) x + (2n + 1)
(B) x +
(C) x + (n + 1)
(D) x −
2
2
18.
An orange colored glass has orange juice and white colored glass has apple juice both of equal
volumes more than 50ml. Now 50ml of the orange juice is taken and poured into the white glass.
After that similarly, 50ml from the white glass is poured into the orange glass. Of the two quantities,
the amount of apple juice in the orange glass and the amount of orange juice in the white glass,
which one is greater ?
(A) apple juice in the orange glass
(B) orange juice in the white glass
(C) cannot say
(D) both are equal
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19.
Ravi is a strange liar. He lies on six days of the week, but on the seventh day he always tells the
truth. He made the following statements on three successive days:
Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it's Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."
On which day does Ravi tell the truth?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
20.
Two boats are crossing the river from opposite sides. When they first meet, they are 720 m from the
near shore. When they reach the opposite shores, they stop for 10 minutes and cross the river again,
but this time they meet 400 m from the other shore. How wide is the river?
(A) 1120 m
(B) 1760 m
(C) 2240 m
(D) None of these
21.
When x13 + 1 is divided by x − 1 , the remainder is
(A) 1
(B) –1
(C) 0
22.
(D) 2
Let P1 be the set of all prime numbers i.e. P1 = {2, 3, 5, 7, 11, …}. Let Pn = {np p ∈ P1} , i.e., the set
of all prime multiples of n. Then which of the following sets is non empty?
(A) P1 ∩ P23
(B) P7 ∩ P21
(C) P12 ∩ P20
(D) P20 ∩ P24
23.
How many triangles are in the figure?
(A) 29
(B) 18
(C) 20
(D) None of these
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24.
Employee’s of a company are made to stand in the rows. If one employee is extra in a row, there
would be 2 row’s less. If one employee is less in a row there would be 3 rows more. Then no. of
employee’s in company is,
(A) 60
(B) 50
(C) 30
(D) 40
25.
The cost price of an article is C and the selling price of the same article is S, where Z is the profit or
loss percentage. If the cost price and selling price both are increased by same amount then which of
the following is true :
(A) Z increases
(B) Z decreases
(C) remains constant
(D) none of these
26.
x
A
B
=
+
, then A – B is
(x + 2)(x + 3) x + 3 x + 2
(A) 4
(B) 5
(C) –6
If
(D) 2
27.
A number lies between 300 and 400. If the number is added to the number formed by reversing the
digits, the sum is 888 and if the unit’s digit and the ten’s digit change places, the new number
exceeds the original number by 9. Find the number.
(A) 339
(B) 341
(C) 378
(D) 345
28.
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours, then speed of current is?
(A) 10
(B) 3
(C) 6
(D) 4
29.
Which combination of letters completes the given series: NRJ, PNP, RJV?
(A) BFT
(B) TFB
(C) TBF
(D) BTF
30.
The earth makes a complete rotation on its axis in 24 hours. How long will it take to turn through
130°?
(A) 500 min.
(B) 520 min.
(C) 600 min.
(D) None
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31.
The sum of three prime numbers is 100. One of them exceeds the other by 36. Find the largest
number
(A) 73
(B) 91
(C) 67
(D) 57
32.
The value of
(A) 4
6 + 6 + 6 + .... is
(B) 3
(C) –2
(D) 3.5
33.
In a row of girls, Nivedita is 15th from the left and Vimla is 23rd from the right. If they interchange
their positions, then Nivedita becomes 18th from the left. Then at what position will Vimla be from
the right.
(A) 25th
(B) 24th
(C) 26th
(D) 20th
34.
Five boys Mahendra, Anjani, Anil, Anand and Alok are sitting in a row. Neither Anil is neighbour of
Anand nor of Anjani. Anil is the neighbour of Alok. If Alok is just in the middle, who is the
neighbour of Mahendra?
(A) Anand
(B) Alok
(C) Anil
(D) Anjani
35.
Ramesh starting from a fixed point goes 15 m towards North and then after turning to his right he
goes 15 m. Then he goes 10, 15 and 15 metres after turning to his left each time. how far is he from
his starting point?
(A) 5 metres
(B) 10 metres
(C) 20 metres
(D) 15 metres
36.
If the numbers which are divisible by 4, from 8 to 84 are written in reverse order then which number
will be at the 7th place.
(A) 28
(B) 32
(C) 64
(D) None of these
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37.
Pointing to a picture of a child Narendra says, “The bother of this child’s mother, is the only son of
my mother’s father.” How is Narendra related to the mother of the child. If Narendra mother has no
sister.
(A) Bother
(B) Father
(C) Uncle
(D) None of these
38.
In the following diagram three classes of population are represented by three figures. The triangle
represents school teachers, the square represents the married persons and the circle represents the
persons living in joint families
E
D
C
B
F
A
School teachers who are married but do not live in joint families are represented by
(A) C
(B) D
(C) B
(D) A
39.
In triangle ABC, with ∠A = 900 , the bisectors of the angles B and C meet at P. The distance from P
to the hypotenuse is 4 2 . The distance AP is :
(A) 8
40.
(B) 4
(C) 8 2
(D) 4 2
In the figure, where AB is tangent to the circle with centre O, find the ratio of the shaded region to
the unshaded region in ∆ OAB .
(A)
2 3−2
π
(B)
3 3− 2
π
(C)
2− 3
π
(D)
3 3
−1
π
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41.
Two squares flowerbeds are placed symmetrically in a rectangular garden as shown in the diagram.
The distance between the beds is y and so is width of the border around the beds on all sides. A seed
blown into the garden by the wind is equally likely to land anywhere in the garden. What is the
probability that it actually lands in a flowerbed?
(A)
42.
2
7
(B)
1
7
(C)
4
7
(D) None of these
A pyramid with a square base has a height of 12 m. The length of the base of the pyramid is 10 m. If
a straight line is drawn from the vertex of the pyramid to any point on the square base, then which of
the following cannot be the length of that straight line?
(A) 12.5 m
(B) 194 m
(C) 181 m
(D) 14 m
43.
The price of wheat falls by 16%. By what percentage a person can increase the consumption of
wheat so that his overall budget does not change?
(A) 16%
(B) 18%
(C) 18.5%
(D) 19%
44.
5% of income of A is equal to 15% of incomes of B and 10% income of B is equal to 20% of income
of C. If C’s income is Rs. 2000, then the total income of A, B and C is:
(A) Rs. 6000
(B) Rs. 14000
(C) Rs. 18000
(D) Rs. 20000
45.
Two candles of equal length start burning at the same instant. One of the candles burns in 5 hrs. and
the other in 4 hrs. By the time one candle is 2 times the length of the other. The candles have already
burnt for :
1
1
1
1
(A) 2 hrs.
(B) 3 hrs.
(C) 3 hrs.
(D) 3 hrs.
2
2
9
3
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46.
2 men and 3 boys together can do a piece of work in 8 days. The same work is done in 6 days by 3
men and 2 boys together. How long would 1 boy alone and 1 men alone take to complete the work
independently:
(A) 40 days, 120 days
(B) 120 days, 40 days
(C) 20 days, 120 days
(D) 120 days, 20 days
47.
5 pens and 6 pencils together cost Rs. 9 and 3 pens and 2 pencils cost Rs. 5. Find the cost of 1 pen
and 1 pencil
(A) Rs. 2, Rs. 0.50
(B) Rs. 1.50, Rs. 0.25
(C) Rs. 1.50, Rs. 0.50
(D) Rs. 2, Rs. 0.25
48.
A person travels in a car from his village to a town at a speed of 50 km/hr for four hours. There he
spends an hour moving about 20 kms. He then returns to his village at a speed 40 km/hr. His average
speed over the whole journey (in km/hr) is:
4
2
(A) 44
(B) 42
(C) 44
(D) 46
9
3
49.
A person goes 2 kms towards East. He then turns right and goes 1 km. He turns again right and goes
3 kms straight. In which direction is how now from his starting place?
(A) North–East
(B) North–West
(C) South–East
(D) South–West
50.
The number of squares formed in the figure given will be
(A) 8
(B) 10
(C) 12
(D) 14
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