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20 Sep 2006, 15:53
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If g is a the square of an integer, then what is the value of g?
(1) Fewer than half of the factors of g are less than 12.
(2) Fewer than half of the factors of g are greater than 12.
(1) Fewer than half of the factors of g are less than 12.
(2) Fewer than half of the factors of g are greater than 12.
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21 Sep 2006, 07:28
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I think it "might" be C.
Statement 1 by itself is not sufficient. The number could 169 or 289 or the square of any prime number greater than 12 and the condition would hold.
Statement 2 by itself is not sufficient. The number could be 16 or 25 and the condition would hold.
Now the question is can we solve this with both together.
By picking different numbers, both these conditions cannot be satisfied simultaneously for any other number except 144. In fact if we pick any square of an integer, it always has an equal number of factors less than its root as it has greater than its root. For example 16 has two factors less than its root 4, i.e. 1 and 2 and 2 factors greater than its root i.e. 8 and 16.
I guess the proof of this would involve the rule that the greatest prime factor of a number is always less than its root. Based on this (and maybe permutations) we should be able to derive the rule on the number of factors
Hence i would say that the number is 144 and solution is C.
Statement 1 by itself is not sufficient. The number could 169 or 289 or the square of any prime number greater than 12 and the condition would hold.
Statement 2 by itself is not sufficient. The number could be 16 or 25 and the condition would hold.
Now the question is can we solve this with both together.
By picking different numbers, both these conditions cannot be satisfied simultaneously for any other number except 144. In fact if we pick any square of an integer, it always has an equal number of factors less than its root as it has greater than its root. For example 16 has two factors less than its root 4, i.e. 1 and 2 and 2 factors greater than its root i.e. 8 and 16.
I guess the proof of this would involve the rule that the greatest prime factor of a number is always less than its root. Based on this (and maybe permutations) we should be able to derive the rule on the number of factors
Hence i would say that the number is 144 and solution is C.
25 Sep 2006, 04:42
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Hey Kevin, can you share the OA for this one? Thanks!
