Rationale: We have 1, 8, 27 and 64 as perfect cubes from 1 to 100. Thus, the probability of picking a perfect cube is 4/100 = 1/25
The answer: (A)
Question: If a number is chosen at random from the set {1, 2, 3, 100}, then the probability that the chosen number is a perfect cube is
Options:
(A) 1/25
(B) 1/2
(C) 4/13
(D) 1/10
(E) 3/10
Reasoning: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Ans: (C)
Question: The length of each side of an equilateral triangle having an area of 43 cm2 is?
Options:
(A) 1/8
(B) 1/9
(C) 1/5
(D) 1/23
(E) 1/2
Rationale: 100 * 100 = 10000
125 * 80 = 10000
The answer: (A)
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
Options:
(A) 10000
(B) 18999
(C) 16990
(D) 16007
(E) 16991
Reasoning: Clearly, 97 is a prime number.
Ans: (D)
Question: Which of the following is a prime number ?
Options:
(A) 90
(B) 94
(C) 96
(D) 97
(E) 98
Rationale: Number of ways = 7!/3!2! = 7X6X5X4X3X2X1/3X2X1X2X1 = 420
The answer: (D)
Question: In how many different ways can the letters of the word 'DIVIDED' be arranged?
Options:
(A) 250
(B) 280
(C) 300
(D) 420
(E) 360
Rationale: This is an alternating addition and subtraction series. In the first pattern, 10 is subtracted from each number to arrive at the next. In the second, 5 is added to each number to arrive at the next.
The answer: (A)
Question: Look at this series: 80, 10, 70, 15, 60, ... What number should come next?
Options:
(A) 20
(B) 23
(C) 25
(D) 30
(E) 35