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# Is integer x square of an integer? 1) Sum of all the factors of x is

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Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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Updated on: 26 Feb 2019, 06:07
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Difficulty:

95% (hard)

Question Stats:

17% (02:04) correct 83% (01:43) wrong based on 35 sessions

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Is integer x square of an integer?

1) Sum of all the factors of x is odd
2) $$x = a^p*b^q$$ where a and b are prime numbers and, p and q are odd integers

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Originally posted by GMATinsight on 26 Feb 2019, 03:54.
Last edited by GMATinsight on 26 Feb 2019, 06:07, edited 1 time in total.
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Re: Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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26 Feb 2019, 05:34
Is integer x square of an integer?

1) Sum of all the factors of x is odd
Just this knowledge is sufficient to eliminate this choice
Logically if only prime factor is 2, the factors will always be odd..
If x is 2, factors are 1 and 2, and sum = 1+2=3. 2 is not a square
If x is 4, factors are 1, 2 and 4, and sum = 1+2+4=7. 4 is a square.
Insuff.

2) $$x = a^p*b^q$$ where a and b are prime numbers and, p and q are odd integers
a and b are prime numbers, and their power p and q are odd,
If a=b, answer is yes, otherwise No
Not sufficient

Combined..
a=b=2, and p=q=3......YES
I can't get any other value which can fit in both so C
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Re: Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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26 Feb 2019, 05:45
chetan2u wrote:
Is integer x square of an integer?

1) Sum of all the factors of x is odd
Just this knowledge is sufficient to eliminate this choice
Logically if only prime factor is 2, the factors will always be odd..
If x is 2, factors are 1 and 2, and sum = 1+2=3. 2 is not a square
If x is 4, factors are 1, 2 and 4, and sum = 1+2+4=7. 4 is a square.
Insuff.

2) $$x = a^p*b^q$$ where a and b are prime numbers and, p and q are odd integers
If a and b are prime numbers, and their power p and q are odd, the number, x, can never be square of any integer.
Even if p and q are same, $$x = a^p*b^q=(ab)^p$$..
We require a EVEN power for the number to be a square. Thus, answer is always NO..

B

Second statement doesn't mention that the Prime numbers are distinct... so $$x =2^3*2^5$$ is also acceptable making the number as perfect square.
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Re: Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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26 Feb 2019, 05:50
GMATinsight wrote:
chetan2u wrote:
Is integer x square of an integer?

1) Sum of all the factors of x is odd
Just this knowledge is sufficient to eliminate this choice
Logically if only prime factor is 2, the factors will always be odd..
If x is 2, factors are 1 and 2, and sum = 1+2=3. 2 is not a square
If x is 4, factors are 1, 2 and 4, and sum = 1+2+4=7. 4 is a square.
Insuff.

2) $$x = a^p*b^q$$ where a and b are prime numbers and, p and q are odd integers
If a and b are prime numbers, and their power p and q are odd, the number, x, can never be square of any integer.
Even if p and q are same, $$x = a^p*b^q=(ab)^p$$..
We require a EVEN power for the number to be a square. Thus, answer is always NO..

B

Second statement doesn't mention that the Prime numbers are distinct... so $$x =2^3*2^5$$ is also acceptable making the number as perfect square.

I think while I was answering you posted. Please tell me a value which gives NO and satisfies both statements.

GMATinsight Also GMAT will never test something in this way as you yourself have missed the point that it will never be NO when combined.
So, OA given is still wrong
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Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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Updated on: 26 Feb 2019, 06:27
chetan2u wrote:
GMATinsight wrote:
chetan2u wrote:
Is integer x square of an integer?

1) Sum of all the factors of x is odd
Just this knowledge is sufficient to eliminate this choice
Logically if only prime factor is 2, the factors will always be odd..
If x is 2, factors are 1 and 2, and sum = 1+2=3. 2 is not a square
If x is 4, factors are 1, 2 and 4, and sum = 1+2+4=7. 4 is a square.
Insuff.

2) $$x = a^p*b^q$$ where a and b are prime numbers and, p and q are odd integers
If a and b are prime numbers, and their power p and q are odd, the number, x, can never be square of any integer.
Even if p and q are same, $$x = a^p*b^q=(ab)^p$$..
We require a EVEN power for the number to be a square. Thus, answer is always NO..

B

Second statement doesn't mention that the Prime numbers are distinct... so $$x =2^3*2^5$$ is also acceptable making the number as perfect square.

I think while I was answering you posted. Please tell me a value which gives NO and satisfies both statements.

GMATinsight Also GMAT will never test something in this way as you yourself have missed the point that it will never be NO when combined.
So, OA given is still wrong

OA is C...

GMAT can not give many things available on gmat club posted from many private (and prestigious) GMAT prep companies too... But I just tried to make a good question and it tricked you too...
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Originally posted by GMATinsight on 26 Feb 2019, 06:11.
Last edited by GMATinsight on 26 Feb 2019, 06:27, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7958
Re: Is integer x square of an integer? 1) Sum of all the factors of x is  [#permalink]

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26 Feb 2019, 06:16
GMATinsight wrote:
chetan2u wrote:

I think while I was answering you posted. Please tell me a value which gives NO and satisfies both statements.

GMATinsight Also GMAT will never test something in this way as you yourself have missed the point that it will never be NO when combined.
So, OA given is still wrong

OA is C... changed...

GMAT can not give many things available on gmat club posted from many private (and prestigious) GMAT prep companies too... But I just tried to make a good question and it tricked you too...

Yes, I did but by the time I posted, I realized it, but then realized there was another fault in the OA.
Also, for me, you too are a reliable institute . and I am sure, you too got tricked by your question by realizing there was more to what you thought the question actually meant.
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Re: Is integer x square of an integer? 1) Sum of all the factors of x is   [#permalink] 26 Feb 2019, 06:16
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