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product of two integers

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product of two integers

by venmic » Sun Nov 13, 2011 12:20 pm
Can the positive integer k be expressed as the product of two
integers, each of which is greater than 1?
(1) k^2 has one more positive factor than k.
(2) 11 < k < 19

A
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Source: — Data Sufficiency |
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by neelgandham » Sun Nov 13, 2011 1:00 pm
Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?
(1) k^2 has one more positive factor than k.
Implies K is a prime number.

K = 3, Factors of 3 = 1,3; K^2 = 9, Factors of 9 = 1,3,9
K = 2, Factors of 2 = 1,2; K^2 = 4, Factors of 4 = 1,2,4
K = 4(Non prime), Factors of 4 = 1,2,4; K^2 = 16, Factors of 16 = 1,2,4,8,16
Now that we know that K is a prime number, we can write the number as a product of two numbers in only one way (K*1). So, positive integer K cannot be expressed as the product of two integers, each of which is greater than 1

Hence, Sufficient
(2) 11 < k < 19
Let K = 12 (4*3) Yes !
Let K = 23 (13*1) No !
Insufficient !

Answer :A
Anil Gandham
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