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).


question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 1 strokes ?
Options:
(A) 1/2
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
answer: Stream of consciousness: Left After 1st stroke = 1/2
So removed = 1- 1/2 = 1/2 The answer is (A).


q: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
Options:
(A) Equal to 3
(B) Less than 3
(C) More than 10
(D) Less than 10
(E) none of these
a: Stream of consciousness: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10 The answer is (C).


question: What will come in place of the x in the following number series? 12, 26, 54, 110, 222, x
Options:
(A) 444
(B) 446
(C) 448
(D) 452
(E) 454
answer: Stream of consciousness: 12
12 × 2 + 2 = 26
26 × 2 + 2 = 54
54 × 2 + 2 = 110
110 × 2 + 2 = 222
222 × 2 + 2 = 446 The answer is (B).


q: A train 495 m long is running at a speed of 63 km/hr. In what time will it pass a bridge 240 m long?
Options:
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43
a: Stream of consciousness: Speed = 63 * 5/18 = 35/2 m/sec
Total distance covered = 495 +240 = 735 m
Required time = 700 * 2/35 = 42 sec The answer is (D).


q: What is the median from the below series
90, 92, 93, 88, 95, 88, 97, 87, and 98
Options:
(A) 85
(B) 89
(C) 92
(D) 98
(E) 100
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median score is 92. The answer is (C).