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If k is an integer, what is the smallest possible value of k

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Senior Manager
Joined: 20 May 2014
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If k is an integer, what is the smallest possible value of k [#permalink]  20 Nov 2017, 10:45
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57% (00:59) correct 42% (01:06) wrong based on 7 sessions
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

A. 2
B. 5
C. 10
D. 15
E. 65

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[Reveal] Spoiler: OA
Director
Joined: 20 Apr 2016
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Re: If k is an integer, what is the smallest possible value of k [#permalink]  01 Dec 2017, 22:27
Bunuel wrote:
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

A. 2
B. 5
C. 10
D. 15
E. 65

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Here let 1060 can be written as = $$2^4 X 65^1$$

to make it perfect square k should be equal = 65 i.e $$2^4 X 65^2$$

Hence option E
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Manager
Joined: 29 Nov 2017
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GRE 1: Q142 V146
WE: Information Technology (Computer Software)
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Re: If k is an integer, what is the smallest possible value of k [#permalink]  10 May 2018, 10:44
I multipled each option to 1040 and took a square root by the calculator and I got the answer in 2.03 min .. E
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Re: If k is an integer, what is the smallest possible value of k [#permalink]  11 May 2018, 04:23
65 as that is what is left post factoring. All the factors should have 2 values atleast
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
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Re: If k is an integer, what is the smallest possible value of k [#permalink]  14 May 2018, 00:47
One should also remember that the exponents of prime factors are even.

or we can solve the problem by taking the prime factorization of 1040 , when we do so we notice the factors of 13 and 5 are not even rather they are only 1 each..

hence we choose the option he because when we multiply 1040 by 65 13 and 5 factors make the exponents of 1040*65 even

hence option is E is correct.
Re: If k is an integer, what is the smallest possible value of k   [#permalink] 14 May 2018, 00:47
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