q: There are 6 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
(A) 90
(B) 120
(C) 225
(D) 180
(E) 200
a: Number of ways of selecting 2 fiction books = 6C2
Number of ways of selecting 2 non fiction books = 6C2
6C2 * 6C2 = 15 * 15 = 225 The answer is (C).
--
q: The average age of A, B and C is 25 years. If the average age of A and C is 29 years, what is the age of B in years ?
Options:
(A) 17
(B) 35
(C) 20
(D) 32
(E) 21
a: Age of B = Age of (A + B + C) Age of (A + C) = 25 3 29 2 = 75 58 = 17 years The answer is (A).
--
q: The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?
Options:
(A) 179 cm and 172 cm
(B) 181 cm and 169 cm
(C) 173 cm and 178 cm
(D) 176 cm and 176 cm
(E) 174 cm and 177 cm
a: Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm. The answer is (B).
--
q: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, 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) 27/280
(D) 3/35
(E) 7/56
a:
P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280. The answer is (C).
--