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If x is an integer, does 2x have twice as many factors as x does? 1)

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GMATinsight
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If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   16 Oct 2021, 05:02
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If x is an integer, does 2x have twice as many factors as x does?

(1) \(x^y\) is divisible by 2 where y is an integer
(2) \(\frac{x}{y}\) is even

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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   Updated on: 18 Oct 2021, 07:22
given x is an integer target does 2*x have twice as many factors as x
#1
\(x^y\) is divisible by 2 where y is an integer
irrespective of the value of y value of x would always be even
so x=2,4,6,8,10,12,16
factors of x for
2=2
4=3
6=4
8=4
10=4
12=6
16= 5
2x for these values ; 4,8,12,16,24,32
factors of 2x would be
4=3
8=4
12=6
24=8
32=6
for all the cases 2x does not have twice as many factors as x does
or x=0 factors of 0 are infinite so 2x can be true as factors of twice as many factors of 0
insufficient
#2
\(\frac{x}{y}\) is even
irrespective of the value of y ; x has to be an even integer
again same as #1 2x does not have twice as may factors as x
or x=3 and y=1/2 ; in this case we get yes as factors of 3 =2 and factors of 2*3 =6 is 4
we get yes and no so #2 is insufficient
from 1 &2 we cannot determine anything conclusively
option E is correct

GMATinsight wrote:
If x is an integer, does 2x have twice as many factors as x does?

1) \(x^y\) is divisible by 2 where y is an integer
2) \(\frac{x}{y}\) is even



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Originally posted by Archit3110 on 16 Oct 2021, 09:24.
Last edited by Archit3110 on 18 Oct 2021, 07:22, edited 2 times in total.
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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   Updated on: 30 Oct 2021, 10:55
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Statement 1 -- Sufficient.
X to the power of y is divisible by 2. For any number to be a multiple of 2, it must be even. And if Y is an integer, X to the power of Y would need to be an even perfect square. X could be positive or negative since any number squared is positive. So test cases for X could be positive or negative.

Some possible values for x and 2x are...

x=-4, -2, 0, 2, 4, 6, 8
2x=-8, -4, 0, 4, 8, 12, 16

If X is -4, X has 5 factors--1, -1, -2, 2, 4, -4--and 2x has 8 factors -- 1, -1, 2, -2, 4, -4, 8, -8. Answer is no, not double.

If X is 0, X has one factor--0--and 2x equals 0, which also has 1 factor. Answer is no, not double.

If X is 4, X has 3 factors--1, 2, 4--and 2X has 4 factors--1, 2, 4, 8. Again, answer is no, not double.

No matter what permissible value of X, 2X never has double the number of factors that X has. Statement 1 is sufficient.

Statement 2 -- Insufficient.
"x/y is even" tells us a few things about x. X could be even, and that would yield the same 'no' as above. But, for this statement, we don't know anything about Y to suggest it must be an integer, so X could also be odd, which can violate this statement. For example, if x/y is 6, X could be 3 and Y could be 1/2. 3 (X) has two factors--1, 3--whereas 6 (2x) has 4 factors--1, 2, 3, 6. This yields a "yes". X could be 4 and Y could be 2, making the answer to the question stem "no", because 2x has 3 factors whereas X has 2 factors. So, statement 2 is insufficient.

The correct answer is A.

Originally posted by xvibrant on 16 Oct 2021, 10:32.
Last edited by xvibrant on 30 Oct 2021, 10:55, edited 5 times in total.
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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   16 Oct 2021, 21:21
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Archit3110
xvibrant

Please reconsider your explanations
Statement 1; x can be 0 or 2 both
Statement 2: x can be 3 and y=1/2 or x may be any even integer too
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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   17 Oct 2021, 07:41
GMATinsight
Sir shouldn't the answer be A ?
As with x with 0 or even number we always get no to target...
GMATinsight wrote:
Archit3110
xvibrant

Please reconsider your explanations
Statement 1; x can be 0 or 2 both
Statement 2: x can be 3 and y=1/2 or x may be any even integer too


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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   18 Oct 2021, 05:43
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Archit3110 wrote:
GMATinsight
Sir shouldn't the answer be A ?
As with x with 0 or even number we always get no to target...
GMATinsight wrote:
Archit3110
xvibrant

Please reconsider your explanations
Statement 1; x can be 0 or 2 both
Statement 2: x can be 3 and y=1/2 or x may be any even integer too


Posted from my mobile device


The question is not just about whether x is even number?

Question is Is "x positive even integer?" because only positive even integer values of x,2x will NOT have twice as many factors as x will have
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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   19 Oct 2021, 01:33
Hi GMATinsight

Thank you for posting out such a wonderful question. However, I also opted for the wrong answer choice. Hence, i request you to please provide the OE or the detailed solution for this question
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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink] New post   02 Feb 2024, 12:03
GMATinsight wrote:
If x is an integer, does 2x have twice as many factors as x does?

1) \(x^y\) is divisible by 2 where y is an integer
2) \(\frac{x}{y}\) is even

Source: https://www.GMATinsight.com


BEST On-Demand QUANT Course: Topicwise Modules | 2000+Qns | Official Qns. | 100% Video solution. Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)



My understanding- 2x will have double factors if X is not a multiple of 2 as in the prime factorization 2^1 will get multiplied. Accordingly I checked with few examples and it worked as statement 1 says X is X is divisible by 2. Hence I've selected A as the answer. Can any of the experts please explain which is A insufficient?

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Re: If x is an integer, does 2x have twice as many factors as x does? 1) [#permalink]
02 Feb 2024, 12:03
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