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14 Mar 2012, 05:36
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D
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Difficulty:
35%
(medium)
Question Stats:
69% (01:18) correct
31%
(01:23)
wrong
based on 131
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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
(1) m is the square of an integer
(2) m is the cube of an integer
14 Mar 2012, 05:41
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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?
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.
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.
18 Mar 2012, 05:34
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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
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
