q: 189. The inside dimensions of a rectangular wooden box
are 12 inches by 14 inches by 16 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) 7
a: Stream of consciousness: 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 16x14width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 14, so the radius will be 7. The answer is (E).
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q: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
a: Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 70 = 20 The answer is (B).
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q: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 84 ounces of this substance?
Options:
(A) 27
(B) 36
(C) 42
(D) 64
(E) 147
a:
Stream of consciousness: 112 ounces of a substance has a volume of 48 cubic inches
84 ounces of a substance has a volume of (48/112)*84 = 36 cubic inches The answer is (B).
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