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If m is a positive integer greater than 1 can m be expressed

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If m is a positive integer greater than 1 can m be expressed [#permalink]

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New post 14 Mar 2012, 05:36
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If m is a positive integer greater than 1, can m be expressed as the product of two integers, each of which is greater than 1?

(1) m is the square of an integer
(2) m is the cube of an integer
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Re: If m is a positive integer greater than 1 can m be expressed [#permalink]

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New post 14 Mar 2012, 05:41
If m is a positive integer greater than 1, can m be expressed as the product of two integers, each of which is greater than 1?

Question basically asks whether m is a prime number: if it is, then it cannot be expressed as the product of two integers, each of which is greater than 1 (definition of a prime number).

(1) m is the square of an integer --> no prime is a perfect square, so m is not a prime and can be expressed as the product of two integers, each of which is greater than 1. Sufficient.

(2) m is the cube of an integer --> no prime is a perfect cube, so m is not a prime and can be expressed as the product of two integers, each of which is greater than 1. Sufficient.

Answer : D.
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Re: If m is a positive integer greater than 1 can m be expressed [#permalink]

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New post 18 Mar 2012, 05:34
Hi Bunuel,

how is stmnt 1 sufficient?

question stem : If m is a positive integer greater than 1, can m be expressed as the product of two integers, each of which is greater than 1?

stmnt 1: m is the square of an integer

if we take m as 4 which is a positive integer >1 , 4 can be expressed as :

-2 * -2 = 4 (or)
2 * 2 = 4

hence M cannot be expressed as product of two integers , each of which is greater than 1
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Re: If m is a positive integer greater than 1 can m be expressed [#permalink]

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New post 18 Mar 2012, 06:08
pappueshwar wrote:
Hi Bunuel,

how is stmnt 1 sufficient?

question stem : If m is a positive integer greater than 1, can m be expressed as the product of two integers, each of which is greater than 1?

stmnt 1: m is the square of an integer

if we take m as 4 which is a positive integer >1 , 4 can be expressed as :

-2 * -2 = 4 (or)
2 * 2 = 4

hence M cannot be expressed as product of two integers , each of which is greater than 1


In your own example you are expressing 4 as the product of 2 and 2, so as the product of two integers each of which is greater than 1 (notice that we are not told that the factors must be distinct).

Hope it's clear.
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Re: If m is a positive integer greater than 1 can m be expressed   [#permalink] 18 Mar 2012, 06:08
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