q: From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x)
Options:
(A) 10
(B) 14
(C) 15
(D) 16
(E) 30
a: Stream of consciousness: Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations The answer is (E).

question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
(A) 198
(B) 288
(C) 360
(D) 396
(E) 484
answer: Stream of consciousness: I will go with C (pending elements to match is 2^2*3^2*10^1 = 360 The answer is (C).

q: Fill in the blank with the correct number in this number series: 5, 15, 7, 12, __, 9, 11,... ?
Options:
(A) 6
(B) 9
(C) 8
(D) 7
(E) 5
a: Stream of consciousness: In this simple alternating subtraction and addition series; The first series begins with 5 and adds 2; the second begins with 15 and subtracts 3, and so on. The answer is (B).

question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 287 sec
(B) 288 sec
(C) 48 sec
(D) 16 sec
(E) 17 sec
answer: Stream of consciousness: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 se The answer is (C).

q: What percent is 120 of 70?
Options:
(A) 133 1/3 %
(B) 134 1/3 %
(C) 135 1/3 %
(D) 140 1/3 %
(E) 171 3/7 %
a: Stream of consciousness: 120/70 = 12/7
12/7 100 = 1200/7 = 171 3/7 % The answer is (E).

q: From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1460
a:
Stream of consciousness: There are 36 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 36 ways. When one person is appointed as leader, we are left with 35 students. Out of these 35 teachers, we can select one class representative. So, a class representative can be selected in 35 ways. Hence, the number of ways in which a leader and class representative can be selected = 36 x 35 = 1260 The answer is (B).