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If x is an integer, is x > 0?

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Source: — Data Sufficiency |

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by Anju@Gurome » Thu Apr 04, 2013 3:36 am
himu wrote:If x is an integer, is x > 0?

x has only one multiple
x has an infinite number of factors
Statement 1: Any non-zero finite integer has infinite number of multiples.
Hence, x must be equal to zero.

Sufficient

Statement 2: Any non-zero finite integer has a finite number of factors.
Hence, x must be equal to zero as zero is multiple of any number.

Sufficient

The correct answer is D.
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by himu » Thu Apr 04, 2013 3:54 am
Thanks Anju for your reply :)

BUt can u pls tell me : for statement I : x has only one multiple : 1 also has single multiple ?

Also can u pls elaborate more on Statement 2 ??

Thanks,
~Himu.
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by Anju@Gurome » Thu Apr 04, 2013 4:11 am
himu wrote:x has only one multiple : 1 also has single multiple ?
Every integer is multiple of 1.
0 = 0*1
2 = 2*1
1000 = 1000*1
himu wrote:Also can u pls elaborate more on Statement 2 ??
Zero is multiple of all integers.
0 = 0*0
0 = 0*1
0 = 0*19879823

Hence, zero has infinite number of factors.

But any other integer has a finite number of factors.
Factors of 2 are : 1 and 2
Factors of 100 are : 1, 2, 4, 5, 10, 20, 25, 50, and 100


Hope that helps.
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by Brent@GMATPrepNow » Thu Apr 04, 2013 5:41 am
It's strange to think of zero as having an infinite number of factors.
Fortunately, the GMAT test-makers typically restrict their Integer Properties questions to positive integers. In fact, I don't believe I've ever seen an official question involving factors/divisors that didn't restrict the values to positive integers only.

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