q: Find the odd man out.10, 25, 45, 50, 66, 70, 80
Options:
(A) 45
(B) 50
(C) 66
(D) 70
(E) 80
a: Stream of consciousness: Each of the numbers except 66 is multiple of 5. The answer is (C).

question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
Options:
(A) 120 m
(B) 200 m
(C) 115 m
(D) 110 m
(E) 150 m
answer: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m The answer is (B).

q: (x +1 )(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d What are the values of a, b, c and d?
Options:
(A) 2
(B) 7
(C) 6
(D) 1
(E) 9
a: Stream of consciousness: (x + 1)(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d
6(x + 1)(x - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
6(x2x2 - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
6(x3+x2x1)6(x3+x2x1) = ax3+bx2+cx+dax3+bx2+cx+d
6x3+6x26x66x3+6x26x6 = ax3+bx2+cx+dax3+bx2+cx+d
Equating the coefficients of like learns on both the sides, a = 6, b = 6, c = -6 and d = -6. The answer is (C).

question: In a is a positive integer smaller than 200 and (14a)/60 is an integer, then a has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
answer: Stream of consciousness: 7a/30 tells us that a is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. The answer is (B).

q: The average of 21 numbers is 25. The average of first ten numbers is 18 and the average of last ten numbers is 32. What is the middle number?
Options:
(A) 195
(B) 175
(C) 184
(D) 201
(E) 188
a: Stream of consciousness: The total of 21 numbers = 21X25 = 525
The total of first 10 and last 10 numbers is = 10 X 14+10 X 19 = 330
So, the middle number is (525 - 330 ) = 195 The answer is (A).

q: For integers U and V, when U is divided by V, the remainder is Zero. Which of the following must be true?
Options:
(A) U and V share no common factors other than 1
(B) UV is odd.
(C) At least one of U and V is odd
(D) The sum U + V is odd
(E) U is odd
a:
Stream of consciousness: At least one of U and V is odd The answer is (C).