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

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.

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

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?

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

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?

Hello,

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

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).

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

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

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)
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