If x is an integer, is x > 0?

[himu]

If x is an integer, is x > 0?

x has only one multiple
x has an infinite number of factors

[Anju@Gurome]

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.

[himu]

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.

[Anju@Gurome]

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

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.

[Brent@GMATPrepNow]

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.

Cheers,
Brent