Reasoning: Clearly, 97 is a prime number.
Ans: (B)
Question: Find a a prime number from below options?
Options:
(A) 84
(B) 97
(C) 98
(D) 100
(E) 102
Rationale: 2 is divisible by 1 and itself So, it is a prime number.
The answer: (B)
Question: Which one of the following is a prime number?
Options:
(A) 55
(B) 2
(C) 74
(D) 25
(E) 21
Reasoning: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 se
Ans: (C)
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 29
(B) 18
(C) 48
(D) 99
(E) 11
Rationale: For example, if there were 4 jellybean colors, the girl would have made a 4x4 arrangement. The boy chopped up each jellybean into 4, the number of pieces would be (4*4)*4 = 64 pieces, which is a cube of 4.
The answer: (D)
Question: A girl is organizing her jellybean collection in which each color has its own row. In each row, there are as many jellybeans as the number of jellybean colors. Her little brother chops each jellybean into the same number of peices as the number of jellybean colors. If the final number of jellybean pieces is m, then:
Options:
(A) m is a perfect square
(B) m is an odd number
(C) m is an even number
(D) m is a perfect cube.
(E) None
Reasoning: No. of ways of choosing 2 chairs out of 4 chairs on which two students will sit = 4C2 = 6
No. of ways of 2 people sitting on selected chairs = 2!
Total ways of making 2 people sit on 2 of 4 chairs = 4C2*2! = 6*2 = 12
Ans: (A)
Question: If there are 4 seats and two students, in how many ways can they be seated?
Options:
(A) 12
(B) 6
(C) 8
(D) 16
(E) 10
Reasoning: The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520.
Ans: (E)
Question: If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is =
Options:
(A) 40320
(B) 27720
(C) 20160
(D) 6720
(E) 2520