# Quantitative Ability (Part 1 of 9)

Directions: Answer the question independently of each other

1. In the X-Y plane, the area of the region bounded by the graph |x + y| + |x-y| = 4 is

1. 8

2. 12

3. 16

4. 20

2. 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?

1. 5

2. 3

3. 2

4. 6

3. 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?

1. 2r (1 + v3)

2. 2r (2 + v3)

3. r (1 + v5)

4. 2r + v3

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

1. 1000 < n < 1200

2. every digit of n is odd

Then how many elements of S are divisible by 3?

1. 9

2. 10

3. 11

4. 12

5. Letx = v4 + v4 − v4 + v4-____ to infinity. Then x equals

1. 3

2. (v13-½)

3. (v13 + ½)

4. v13

6. 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?

1. 15

2. 14

3. 12

4. 10

7. 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 person-to-person 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?

1. 5

2. 10

3. 9

4. 15

8. 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:

1. 10

2. 12

3. 14

4. 16

9. 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

1. 10

2. 0

3. 7

4. 1

10. Consider a triangle drawn on the X-Y 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

1. 780

2. 800

3. 820

4. 741

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

1. 100 < A < 299

2. 106 < A < 305

3. 112 < A < 311

4. 118 < A < 317

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

1. 399 − 200

2. 399 + 200

3. 3100 − 200

4. 3100 + 200

13. Let S be the set of five-digit 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?

1. 228

2. 216

3. 294

4. 192

14. The rightmost non-zero digit ofthe number 302720 is

1. 1

2. 3

3. 7

4. 9

15. Four points A, B, C and D lie on a straight line in the X-Y 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

1. 3v2

2. 1 + p

3. 4p/3

4. 5

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

1. -1

2. -0.5

3. 0

4. 1

17. 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

1. 81

2. 16

3. 18

4. 9