# PRACTICE TEST 2:QUANTITATIVE ABILITY

1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

(1) 2 ≤ x ≤ 6

(2) 5 ≤ x ≤ 8

(3) 9 ≤ x ≤ 12

(4) 11≤ x ≤ 14

(5) 13 ≤ x ≤ 18

Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f (5) = −3f (2) and that 3 is a root of f(x) = 0.

1. What is the other root of f(x) = 0?

(1) −7

(2) − 4

(3) 2

(4) 6

2. What is the value of a + b + c?

(1) 9

(2) 14

(3) 13

(4) 37

3.In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

If group B contains 23 questions, then how many questions are there in group C?

(1) 1 (2) 2 (3) 3 (4) Cannot be determined

If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?

(1) 11 or 12 (2) 12 or 13 (3) 13 or 14 (4) 14 or 15

4.A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

(1) 4 (2) 8 (3) 16 (4) 32

5.The remainder, when (15^23 + 23^23) is divided by 19, is

(1) 4 (2) 15 (3) 0 (4) 18

6. Let u = (log2 x)2 – 6 log2 x + 12 where x is a real number. Then the equation xu = 256, has

(1) no solution for x (2) exactly one solution for x (3) exactly two distinct solutions for x (4) exactly three distinct solutions for x

7. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

(1) 12 × 81 (2) 16 × 192 (3) 20 × 125 (4) 24 × 216

8.In a ballot process, 900 votes more were polled in favour of a resolution than were polled against it. It was also noticed that the number of votes polled against the resolution was 30 percent of the total number of votes polled. If all the votes polled were valid and each vote was either in favour of the resolution or against it, find the total number of votes polled.

(1) 3400 (2) 2250(3) 2000 (4) 1150

9.The letters of the English alphabet, in the order A to Z, are made to represent 26 numbers which are in Arithmetic Progression. The sum of the numbers representing A, C and E is 36 while that of A, C, E and G is 60. What is the sum of the numbers representing B, D, F and H?

(1) 96 (2) 66(3) 72 (4) 84

10.Sameer and Sumer started running from the same point in opposite directions on a circular track of length 120 m. Their speeds are 20 m/s and 40 m/s respectively. After every second, Sameer increases his speed by 2 m/s whereas Sumer decreases his speed by 2 m/s. How many times would they have met on the track by the time Sumer comes to rest?

(1) 2 (2) 5(3) 4(4) 10