q: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder X when N is divided by 30?
Options:
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
a: Stream of consciousness: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder X when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1. The answer is (C).

question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
(A) 13
(B) 18
(C) 40
(D) 37
(E) 25
answer: Stream of consciousness: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong. The answer is (C).

q: 189. The inside dimensions of a rectangular wooden box
are 12 inches by 14 inches by 16 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
a: Stream of consciousness: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 16x14width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 14, so the radius will be 7. The answer is (E).

question: What is the greatest positive integer x such that 2^x is a factor of 8^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
answer: Stream of consciousness: 8^10 = (2^3)^10 = 2^30 The answer is (E).

q: 252 can be expressed as a product of primes as:
Options:
(A) 2 x 2 x 3 x 3 x 7
(B) 2 x 2 x 3 x 3 x 8
(C) 2 x 2 x 3 x 3 x 6
(D) 2 x 2 x 3 x 3 x 1
(E) 2 x 2 x 3 x 3 x 2
a: Stream of consciousness: Clearly, 252 = 2 x 2 x 3 x 3 x 7. The answer is (A).

q: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
Options:
(A) 297
(B) 268
(C) 300
(D) 179
(E) 172
a:
Stream of consciousness: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300 The answer is (C).