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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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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.
Math Expert V
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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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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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
GMATinsight, please look into your OA. It cannot be E. B will be the answer

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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GMATinsight
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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Math Expert V
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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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
GMATinsight, please look into your OA. It cannot be E. B will be the answer

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
_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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GMAT: INSIGHT
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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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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
GMATinsight, please look into your OA. It cannot be E. B will be the answer

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... _________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

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 V
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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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.
_________________ 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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