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This is the answer in the book but I just don't get it..

Statement (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x. Testing numbers, we can see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore, x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2. SUFFICIENT. Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime number is odd, and x is even. However, this does not tell us which even number x could be. INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the ques- tion, but Statement (2) is insufficient.

Re: If x > 1, what is the value ofinteger x? [#permalink]
18 Mar 2011, 13:39

even i was confuse for the first time. But I think the answer explainations tells, if say x = 5, then it needs 5 unique factor, but for 5 it is only 1 and 5. For 4 it is 1,2, and 4. So for any number greater than 2 there is no way you can have as many factor as the number itself. hence it should be 2. I hope I interpreted right, but as I said it is a confusing question.

Re: If x > 1, what is the value ofinteger x? [#permalink]
18 Mar 2011, 14:34

1

This post received KUDOS

Well here is how i would do it.

1. x has x factors

meaning if you take any integer , that should have that many factors

1 has 1 factor (i.e 1 , meets the criteria) 2 has 2 factors (i.e 1 and 2) 3 has 2 factors (i.e 1 and 3, doesnt meet the criteria, to satisfy this should have had 3 factors)

take any other number lets say 17 , to meet this criteria this should have 17 factors. not satisfied.

so only 1 and 2 satisfies the condition, then again in the question it says x has to be greater than 1 . so that rules out 1 . Hence x =2 .

So sufficient. 2. x + ( prime >x )has to be odd

primes (2,3,5,7,11....)

2+ (prime >2) = 2 +3 = odd (x could be 3) 2+5 = odd (x could be 5)

Not sufficient as there are more possible values for x.

Re: If x > 1, what is the value ofinteger x? [#permalink]
18 Mar 2011, 18:13

2

This post received KUDOS

Expert's post

l0rrie wrote:

If x > 1, what is the value of integer x?

(1) There are x unique factors of x. (2) The sum of x and any prime number larger than x is odd.

First of all, it is not a very straight forward question. Definitely needs some thinking so relax...

Ques: What is the value of x? So we are looking for a single value of x.

First consider statement 2 since it is easier. x + prime number greater than x = odd There will be many many prime numbers greater than x. All prime numbers are odd except 2. So if you can add any prime number greater than x to x and get an odd number, it means x must be even. (because Even + Odd = Odd) So all statement 2 tells you is that x is even. It could be 2 or 4 or 6 etc

Now look at statement 1. There are x unique factors of x. Think of the first number greater than 1. 2 has 2 unique factors: 1 and 2 ( 2 is a prime number) What about 3? It has 2 unique factors: 1 and 3 (a prime number) 4 has 3 unique factors: 1, 2 , 4 Is it possible that any greater number x has x unique factors? No. Why? For x to have x unique factors, each number from 1 to x must be a factor of x. Say if 10 had 10 unique factors, each number 1, 2, 3, 4, 5..., 9,10 would have to be a factor of 10 (because factors are always positive integers) But can 9 be a factor of 10 i.e. can (x-1) be a factor of x? No. 2 consecutive positive integers share only one common factor i.e. 1. Why? Check out the post given below for the answer: question-from-practice-exam-78880.html#p847817

So statement 1 is enough to tell us that x is 2.
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Re: If x > 1, what is the value ofinteger x? [#permalink]
19 Mar 2011, 02:34

Thanks everyone!! Really much appreciated, I get it now.. This has been extremely helpful.. I need to do a GMAT but it's been 6 years since I've studied maths.. And even in high school I was horrible so i'm really stressed about this.. Hopefully I'll get better haha.. Again, thanks!

Re: If x > 1, what is the value ofinteger x? [#permalink]
19 Sep 2013, 13:37

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Re: If x > 1, what is the value of integer x? [#permalink]
19 Sep 2013, 23:34

Expert's post

If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.