Quantitative Ability (Part 1 of 9)
Directions: Answer the question independently of each other

In the XY plane, the area of the region bounded by the graph x + y + xy = 4 is

8

12

16

20
Answer: c


Let g (x) be a function such that g (x + I) + g (x − 1) = g (x) for every real x. Then for what value of p is the relation g (x + p) = g (x) necessarily true for every real x?

5

3

2

6
Answer: d


P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

2r (1 + v3)

2r (2 + v3)

r (1 + v5)

2r + v3
Answer: a


Let S be a set of positive integers such that every element n of S satisfies the conditions

1000 < n < 1200

every digit of n is odd
Then how many elements of S are divisible by 3?

9

10

11

12
Answer: a


Letx = v4 + v4 − v4 + v4____ to infinity. Then x equals

3

(v13½)

(v13 + ½)

v13
Answer: c


A telecom service provider engages male and female operators for answering 1000 calls per day. Amale operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wages ofRs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answer. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

15

14

12

10
Answer: d


Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over persontoperson phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?

5

10

9

15
Answer: c


A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number ofthe white tiles is the same as the number of red tiles. A possible value ofthe number of tiles along one edge of the floor is:

10

12

14

16
Answer: b


Let n! = 1 × 2 × 3 x ____ x n for integer n > 1. If p = 1! + (2 × 2!) + (3 × 3!) + … + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of

10

0

7

1
Answer: d


Consider a triangle drawn on the XY plane with its three vertices at (41, 0) (0, 41), and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

780

800

820

741
Answer: a


The digits of a threedigit number A are written in the reverse order to form another threedigit number B. If B> A and BA is perfectly divisible by 7, then which of the following is necessarily true?

100 < A < 299

106 < A < 305

112 < A < 311

118 < A < 317
Answer: b


If a1 = 1 and an + 1 − 3an + 2 = 4n for every positive integer n, then a100 equals

399 − 200

399 + 200

3100 − 200

3100 + 200
Answer: c


Let S be the set of fivedigit numbers formed by the digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

228

216

294

192
Answer: b


The rightmost nonzero digit ofthe number 302720 is

1

3

7

9
Answer: a


Four points A, B, C and D lie on a straight line in the XY plane, such that AB = BC = CD and the length of AB is 1 meter. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points Band C. The ant would not go within one meter of any insect repellent. The minimum distance in meters the ant must traverse to reach the sugar particle is

3v2

1 + p

4p/3

5
Answer: b


If x > y and y > 1, then the value of the expression logx (x/y) + logy (y/x) can never be

1

0.5

0

1
Answer: d


For a positive integer n, let Pn denote the product of the digits of n, and sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which Pn + sn = n is

81

16

18

9
Answer: d


Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 ern by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is

4

5

6

7
Answer: c
