QUANTITATIVE ABILITY

Directions for questions 1 to 6: Select the correct alternative from the given choices.

1. Two trains cross each other in time T, when they are travelling in opposite directions. The faster train completely overtakes the slower train in time t if they are travelling in the same direction. If the trains are equal length, how long will the faster train take to completely overtake the second train, when the first one is in rest?

Tt T – t

(1) ---------- (2) ---------

2(T+ t) T + t

2Tt

(3) T + t (4) ---------

T + t

C

O

B

A

2. O is the centre of a semicircle on AB as diameter. A circle with centre C is drawn to touch this semicircle and also other semicircles drawn on OA & OB as diameters. Find the radius of circle with centre C if OA = 6.

(1) 2

(2) 3

(3) 3.5

(4) 4

3. 13 men and 7 boys can finish a job in
7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job?

(1) 42 (2) 54 (3) 21 (4) 63

4. Find the probability of getting a larger number than the previous number every time, when an unbiased die is thrown three times.

(1) 1/18 (2) 15/216

(3) 25/216 (4) 5/54

5. What does the following graph represent?

0 1 2 3

5

4

3

2

1

(1) y = , x ¹ k, k is a whole number

(2) y = x - k, k is a whole number such that
k - 1 £ x < k

(3) y = x + k, k is a whole number such that
k £ x < k + 1

(4) y = [x] where [x] is a whole number n such that k £ x < k + 1

6. Two glasses contain milk and water. In the first glass the ratio of milk to water is 3 : 2 and in the second glass the ratio of milk and water is reverse of that in first glass. What part of the mixture from first glass should be drawn out and added to the second glass, so that milk and water will be in equal quantities in the second glass?

(1) 1/3 (2) 1/4 (3) 2/5 (4) 1/2