question: A train 520 meters long is running with a speed of 34 kmph. The time taken by it to cross a tunnel 280 meters long is?
Options:
(A) 287 sec
(B) 89 sec
(C) 48 sec
(D) 16 sec
(E) 17 sec
answer: Stream of consciousness: D = 580 + 280 = 800
S = 34 * 5/18 = 9 mps
T = 800/9 = 89 sec The answer is (B).

q: There are 23 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
a: Stream of consciousness: {Total} = {M} + {N} - {Both}
{Total} = 23 + 28 - 12 = 39. The answer is (A).

question: The edge of a cube is 5a cm. Find its surface?
Options:
(A) 24a8
(B) 150a2
(C) 24a1
(D) 24a2
(E) 24a7
answer: Stream of consciousness: 6a2 = 6 * 5a * 5a = 150a2 The answer is (B).

q: From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x,p,q), etc and (x,y)=(y,x)
Options:
(A) 10
(B) 14
(C) 45
(D) 63
(E) 80
a: Stream of consciousness: Another way: Any letter (x, y, z, w, p, q) can be included or not. So, we have 2^6 combinations - 1 empty combination = 63 combinations The answer is (D).

question: What is the are of an equilateral triangle of side 16 cm?
Options:
(A) 645
(B) 649
(C) 443
(D) 643
(E) 143
answer: Stream of consciousness: Area of an equilateral triangle = 3/4 S2
If S = 16, Area of triangle = 3/4 * 16 * 16 = 643 cm2; The answer is (D).

question: Find the smallest number which should be multiplied with 560 to make it a perfect square.
Options:
(A) 60
(B) 55
(C) 45
(D) 25
(E) 35
answer:
Stream of consciousness: 560 = 2*2*2*2*7*5
Required smallest number = 7 * 5 = 35
35 is the smallest number which should be multiplied with 560 to make it a perfect squar The answer is (E).