q: 45 pupil,out of them 12 in debate only and 22 in singing only.then how many in both?
Options:
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
a: Stream of consciousness: The intersection for two = 45 - 12 - 22 = 11 play both games. The answer is (C).


question: A boy runs 200 metres in 60 seconds. What is his speed ?
Options:
(A) 12 km/hr
(B) 24 km/hr
(C) 13 km/hr
(D) 14 km/hr
(E) 16 km/hr
answer: Stream of consciousness: 200/60 * 18/5 = 12 km/hr The answer is (A).


q: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 288
(B) 150
(C) 77
(D) 166
(E) 1812
a: Stream of consciousness: 1/2 * 20(9 + 6) = 150 cm2 The answer is (B).


question: From among the 31 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) 930
answer: Stream of consciousness: There are 31 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 31 ways. When one person is appointed as leader, we are left with 35 students. Out of these 30 teachers, we can select one class representative. So, a class representative can be selected in 30 ways. Hence, the number of ways in which a leader and class representative can be selected = 31 x 30 = 930 The answer is (E).


q: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/280
(C) 3/280
(D) 4/56
(E) 77/280
a: Stream of consciousness: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 77/280. The answer is (E).


q: How much 45% of 60 is greater than 35% of 40?
Options:
(A) 18
(B) 13
(C) 15
(D) 17
(E) 71
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: (45/100) * 60 – (35/100) * 40
27 - 14 = 13 The answer is (B).