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by das.ashmita » Wed Aug 22, 2012 7:15 am
Can someone please suggest the shortest approach for this question?

An integer between 1 and 300, inclusive, is chosen at random. What is the probability that the integer so chosen equals an integer raised to an exponent that is an integer greater than 1?
A 17/300
B 1/15
C 2/25
D 1/10
E 3/25

OA 2/25
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by GaneshMalkar » Wed Aug 22, 2012 7:32 am
x^2 : 1 = 1, 2 = 4, 3 = 9, 4 = 16, 5 = 25, 6 = 36, 7 = 49, 8 = 64, 9 = 81, 10 = 100, 11 = 121, 12 =144, 13 = 169, 14 = 196, 15 = 225, 16 = 256, 17 = 289 === 17 numbers

x^3 : 2 = 8, 3 = 27, 5 = 125, 6 = 216 == 4 numbers

x^5 : 2 = 32, 3 = 243 == 2 numbers

x^7 : 2 = 128 == 1 number


We don't have to consider numbers raised to even powers greater than 2 since they have already been counted.


Total = 24

Probability = 24/300 = 2/25
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by cypherskull » Wed Aug 22, 2012 11:37 am
Good problem and great solution provided by Ganesh..!! I'd have definitely marked A. Thanks for the solution!
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Sunit

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