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Is the positive Integer x a perfect square? 1) Sum of all factors of

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Is the positive Integer x a perfect square? 1) Sum of all factors of  [#permalink]

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New post 19 Jan 2018, 06:30
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A
B
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Difficulty:

  75% (hard)

Question Stats:

42% (01:22) correct 58% (01:19) wrong based on 75 sessions

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Is the positive Integer x a perfect square?

1) Sum of all factors of x is odd
2) Number of all factors of x is odd

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Re: Is the positive Integer x a perfect square? 1) Sum of all factors of  [#permalink]

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New post 19 Jan 2018, 07:15
B.

A doesnt fit. For a number to be perfect square only the number of factors has to be odd not the sum. Insufficient
B exactly states the rule. sufficient
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Re: Is the positive Integer x a perfect square? 1) Sum of all factors of  [#permalink]

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New post 22 Jan 2018, 10:51
1
GMATinsight wrote:
Is the positive Integer x a perfect square?

1) Sum of all factors of x is odd
2) Number of all factors of x is odd



Statement 2:

It is a property worth remembering:

All perfect square has odd number of factors and vice versa.

4 has positive factors: 1,2 ,4..Sum = 7

9 has positive factors: 1,3 ,9..Sum = 13

Sufficient

Statement 1:

Use one example from above

4 has positive factors: 1,2 ,4..Sum = 7..Answer is Yes

2 has positive factors: 1,2..Sum = 3 .....Answer is No

Insufficient

Answer B
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Re: Is the positive Integer x a perfect square? 1) Sum of all factors of  [#permalink]

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New post 03 Mar 2018, 10:55
Statement 1: a perfect square will have odd number of odd factors and even number of even factors. Therefore odd*odd + even*even = odd , however, vice versa is not true. It isn't necessary that if sum of factors is odd then it is a perfect square. Say number 6. 6 = 3*2, sum of factors = 5 but is 6 a perfect square. NO.
Insufficient

Statement 2: the perfect square will always have odd no of factors. How?

a^2*b^2 = total no of factors = 3*3 = 9 ( odd)
a^4*b^4 = total no of factors = 5*5= 25 ( odd)
Square of Prime number has 3 factors a,1,a^2
Sufficient

Hence Ans = B

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Re: Is the positive Integer x a perfect square? 1) Sum of all factors of &nbs [#permalink] 03 Mar 2018, 10:55
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