4. A = {179, 180, 181,…..,360}. B is a subset of A such that sum of no two elements of B is divisible by
9. The number of elements in B cannot exceed
(1) 102 (2) 81 (3) 82 (4) 101
7. If Ramu and Krishna work on alternate days to complete a work, then the work gets completed in
exactly 24 days. If R and K denote the number of days required by Ramu and Krishna respectively to
complete the work independently, then how many ordered pairs of integral values of R and K are
possible?
(1) 14 (2) 8 (3) 15 (4) 7
9. How many four-digit numbers, having distinct digits, using the digits 1, 2, 3, 4 and 5 can be formed
such that the numbers formed are divisible by each of the digits used in the number?
(1) 1 (2) 2 (3) 4 (4) None of these
10 10. Boxes of 2 types viz. A and B are used for packing balls of 2 different colours. Each of the type A boxes can hold a maximum of 17 blue balls or 19 green balls, and each of the type B boxes can hold a
maximum of 18 blue balls or 23 green balls. When all the boxes of type A are to be completely filled
with blue balls and all the boxes of type B with green balls, the total number of balls required is 566. But
when the boxes of type A are to be completely filled with green balls and the boxes of type B with blue
balls, the total number of balls required is 49 less. How many boxes are there? (All balls of the same
colour are identical.)
(1) 28 (2) 30 (3) 26 (4) 32
11. The functions f(x) and g(x) are defined as: f(x) = f(x – 1) + x and g(x) = g(x – 1) + f(x), where x is an
integer greater than or equal to 1. If f(0) = 0, then the value of k, for which g(k) – g(4) = g(10) – g(8),
is
(1) 8 (2) 6 (3) 9 (4) 12
12. In a community of 80 members, 30 could speak French and 40 Urdu. 20 new members joined this
community, out of which 9 could speak both Urdu and French and 11 could speak exactly one of these
two languages. As a result, the fraction of the members of the community who could speak both Urdu
and French doubled. The number of members who could speak exactly one of these two languages,
finally, is
(1) 58 (2) 63 (3) 69 (4) 75
13. When I left home for office on a particular day my father’s watch showed 7:00 PM, and when I reached
my office my watch showed 7:50 PM. Next day in the morning when my father’s watch showed 6:00
AM, my watch showed 7:30 AM. If my father’s watch runs at normal speed and my watch gains 5
minutes per hour, then the time taken by me to reach my office from home, on that day, was closest to
(1) 15 minutes (2) 13 minutes 38 seconds
(3) 13 minutes 50 seconds (4) 14 minutes 50 seconds
14. xy + zy = 37 and xz + zy = 72. Find the number of ordered triplets (x, y and z) such that x, y and z are
positive integers.
(1) 1 (2) 3 (3) 2 (4) 0
15. Gattu had 130 lts of blue paint,160 lts of red paint, and 180 lts of white paint. He painted four equally
sized stripes on a wall, making a blue stripe, a red stripe, a white stripe and a pink stripe. Pink paint is a
mixture of red and white paints. When Gattu finished, he had equal amount of blue, red, and white
paints left. If he has to paint four more stripes of the same dimensions on another wall in exactly the
same way, then which of the following is true?
(1) Gattu requires 30 lts of blue paint, 0 lts of red paint and 40 lts of white paint
(2) Gattu requires 30 lts of blue paint, 60 lts of red paint and 60 lts of white paint
(3) Gattu requires 30 lts of blue paint, 60 lts of red paint and 80 lts of white paint
(4) Gattu requires 80 lts of blue paint, 110 lts of red paint and 130 lts of white paint
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LR
DIRECTIONS for Questions 51 to 53: Answer the questions on the basis of the information given below.
Five people namely Ajay, Anand, Anup, Akash and Arjun work in the same company. Each one of them
owns exactly one of the vehicles from a car, a bicycle, a scooter, a truck and a bus, not necessarily in the
given order. Each of the people has a different height. Exactly two out of the five people are brothers.
Further it is known that:
I. The shortest person does not have a bicycle and the tallest person has neither a car nor a scooter.
II. None of the two brothers is the tallest or the shortest among the given 5 people.
III. Akash has a car and is taller than at least three of the given people.
IV. Ajay does not have a bus. He is taller than exactly one of the two brothers.
V. Anup has a scooter and is not the shortest.
51. Which of the following are the two brothers?
(1) Arjun and Akash (2) Akash and Anup
(3) Ajay and Akash (4) Cannot be determined
52. If Arjun is the shortest among the five people and has a bus, then which of the following statements is
definitely true?
(1) Ajay has a bicycle and is one of the brothers.
(2) Anand is the tallest and has a truck.
(3) Ajay has a truck and is taller than exactly 2 of the given 5 people.
(4) None of these.
53. How many of the following statements, if provided independently, would be sufficient to determine
the owner of each of the vehicles?
A. Anand is the shortest among the five people and has a truck.
B. Ajay has a truck and Anand is the tallest.
C. Anand is the tallest among the five people and has a truck.
D. Arjun is not the tallest among the five people and does not have a bus.
(1) 2 (2) 1 (3) 4 (4) 3
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DI
