q: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 14 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Options:
(A) 2,060
(B) 1,320
(C) 545
(D) 364
(E) 220
a: 14*13*12/3*2*1 = 364 The answer is (D).
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q: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 12 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
(A) 10 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 20 min.
a: The ratio is 2:3 = gym:ride, so (12)(3/2) = 18 minutes at the gym, and 18 + 12 = 30 minutes exercise, so (2/3)(30) = 20 minutes yoga. The answer is (E).
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q: Antony, Ben, and Charles 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) 3/35
(E) 68/280
a: 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 = 68/280. The answer is (E).
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q: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
Options:
(A) 190 metres
(B) 160 metres
(C) 180 metres
(D) 120 metres
(E) 200 metres
a:
Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36) 18 = 200 m
Distance covered is equal to the length of the train = 200 m The answer is (E).
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