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: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
(A) 10
(B) 26
(C) 12
(D) 24
(E) 48
a: Stream of consciousness: 1/8 + 1/24 = 1/6
6 * 2 = 12 The answer is (C).

question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.165. Find the unknown rate of two towels?
Options:
(A) A) 400
(B) B) 450
(C) C) 500
(D) D) 550
(E) E) 600
answer: Stream of consciousness: 10 * 150 = 1650
3 * 100 + 5 * 150 = 1050
1650 1050 = 600 The answer is (E).

q: Twelve coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^9
(B) 2^11
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
a: Stream of consciousness: Fix the third coin as H. The remaining 11 coins have 2^11 outcomes. The answer is (B).

question: A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
(A) 1
(B) 4
(C) 9
(D) 11
(E) 13
answer: Stream of consciousness: 221 + 43 = 264/17 = 9 (Remainder) The answer is (C).

question: How long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length?
Options:
(A) 16.5
(B) 16.0
(C) 16.4
(D) 14
(E) 16.1
answer:
Stream of consciousness: D = 110 + 170 = 280 m
S = 72 * 5/18 = 20
T = 280 * 1/20 = 14 sec The answer is (D).