question: If c and d are unique prime integers, which of the following must be even?
Options:
(A) cd
(B) 2c2d
(C) c2d
(D) 2cd
(E) cd^2
answer: Stream of consciousness: Any number multiplied by 2 has to be an even number The answer is (B).

q: The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2 m on all its sides. The area of the verandah is :
Options:
(A) 124 m2
(B) 120 m2
(C) 108 m2
(D) 58 m2
(E) None of these
a: Stream of consciousness: Area of the outer rectangle = 19 16 = 304 m2
Area of the inner rectangle = 15 12 = 180 m2
Required area = (304 180) = 124 m2 The answer is (A).

question: What is the area of a square with perimeter 16P ?
Options:
(A) 16p^2
(B) 4P
(C) P^2/4
(D) P/16
(E) P^2/16
answer: Stream of consciousness: Each side is 4p
A = (4p)^2 = 16(p^2) The answer is (A).

q: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 87
(C) 26
(D) 21
(E) 14
a: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec The answer is (A).

question: The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
Options:
(A) 19
(B) 20
(C) 35
(D) 31
(E) 27
answer: Stream of consciousness: The total of nine numbers = 9X15 = 135
The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100
So, the middle number is (135 - 100 ) = 35 The answer is (C).

question: Find the average of the first 23 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
answer:
Stream of consciousness: Average of the first 'n' natural numbers = (n + 1)/2
We get (23 + 1)/2 = 12 The answer is (E).