A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 1/50
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
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The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) (1/5) (2/5) = 1/50 So the answer is: (A).
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189. The inside dimensions of a rectangular wooden box
are 8 inches by 10 inches by 12 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
--
Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 12x10 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 10, so the radius will be 5. So the answer is: (C).
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Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
(A) 12 min
(B) 6 min
(C) 4 min
(D) 8 min
(E) 10 min
--
1/8 + 1/24 = 1/6
6 * 2 = 12 So the answer is: (A).
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