If x is an integer, is x 0?

Question

If x is an integer, is x > 0?

1. x has only one multiple
 2. x has an infinite number of factors

oss198 · Accepted Answer

1) Every number different from 0 has a infinite number of multiple. Ex the mutiples of 2 are 2, 4, 6, 8 etc.
But 0 will only have one multiple : 0 itself. 
For example :  0*1 = 0 ,  0*2=0 ,  0*3=0. 
So x=0. Sufficient.

2) Every integer has a finite number of factors. example : 2 has 2 and 1. 3 has 3 and 1. 4 has 4, 2 and 1. etc...
The only number with an infinite number of factors will be 0. example :  0 = 1*2*3*4*5*(etc)* 0  
so x=0. Sufficient.

Answer D

gmathunk · Answer

It is given that x>0, then why are we considering the condition of x=0 and answering?
That's true x=0 is the only possible solution but still it's against the given question. Or the question itself is flawed?

Sagar5999 · Answer

Hello,

The only thing that the question says is X is an integer.It asks whether X > 0 .

Thanks

EMPOWERgmatRichC · Answer

Hi gmathunk,

When dealing with DS questions, you have to pay careful attention to the information that you're given and the QUESTION that is asked. Organization and note-taking are key here. Your task is to determine whether a given Fact (when combined with any information that you were given from the prompt) is enough to definitively answer the given question or not.

Here, we're told that X is an INTEGER. The QUESTION asks if it is greater than 0. This is a YES/NO question.

Thus, while we know that X is a whole number, it could be a positive or negative integer and it could even be 0. By working with each of the two individual Facts, you can determine that X MUST be 0 in each case, so you CAN definitively answer the question (the answer is ALWAYS NO).

GMAT assassins aren't born, they're made,
Rich

ajdse22 · Answer

Hi, Thanks for your post. I want to study if it relevant to the solution that x is an integer. If it was not told, what difference does it cause to the solution? The first statement will still be sufficient. Let us consider a fraction 0.5 . Now we know that it has more than one multiple. The second statement will be insufficient because we now have zero and a value such as 1/2. 1/2 can have infinite factors. For example 1/2p is a factor of 1/2 for any p as long it is multiplied by p. Please let me know if I am in the right direction

BillyZ · Answer

Official solution from Veritas Prep.

Solution: D

The only integer that has exactly one multiple is 0; every other integer has an infinite number of multiples, so statement (1) is SUFFICIENT. Zero is also the only integer that has an infinite number of factors – zero divided by anything yields an integer result – so statement (2) is also SUFFICIENT. (If you were wondering about infinity itself as a possibility for statement (2), infinity isn’t an integer because it cannot be represented in terms of digits.) (D)

Nunuboy1994 · Answer

Interesting question

Statement 1

X must be 0 because only 0 is the only integer that has one multiple

Statement 2

Only 0 can have an infinite number of factors

bumpbot · Answer

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If x is an integer, is x > 0?

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GMAT Data Sufficiency (DS) Questions

If x is an integer, is x > 0?

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