q: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
a: Stream of consciousness: Distance covered by the car = 80 10 = 800 km
\ Speed = 8008 = 100 km/hr
\ Speed gain = 100 80 = 20 km/hr The answer is (E).
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q: A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue?
Options:
(A) 5/19
(B) 9/20
(C) 1/57
(D) 15/57
(E) 15/684
a: Stream of consciousness: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57 The answer is (C).
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q: 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
a:
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).
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