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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]

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18 Mar 2011, 14:39

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]

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18 Mar 2011, 15:34

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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.

(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. _________________

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

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19 Mar 2011, 03:34

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!

If x > 1, what is the value of integer x? (1) There are x unique factors of x. ( what does that mean ?????? ) (2) The sum of x and any prime number larger than x is odd. thanks

They could have worded Statement 1 better, but it's just trying to tell you how many positive divisors x has. Here we learn that x has x positive divisors. If you just imagine a number for x (e.g. imagine the phrase "10 has 10 positive divisors", clearly absurd) you can probably see quickly that this is almost never true. For x to have x positive divisors, x would need to be divisible by *every* integer from 1 up to x inclusive. That will only happen if x = 1 or x = 2. Since x > 1, x must be 2, and Statement 1 is sufficient.

Statement 2 will be true for any even value of x (since any prime larger than x will be odd if x > 2), so is not helpful.

The answer is A. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Option A says x unique factors of x ... In my opinion there are only two integers whose unique factors are equal to themselves They are 1 = 1 and 2 = 1,2 And We need an integer greater that 1 so it has to be 2 Thus sufficient

Option B tells us that x+prime num larger that x = odd therefore 2 + 3 = 5 ...odd also if we suppose x= 4 then 4 +5 = 9...odd ....

therefore x can be any even number greater than 1 ...hence this option is insufficient

If x>1, what is the value of integer x? 1) There are x [#permalink]

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10 Aug 2011, 18:45

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.

The MGMAT book explains the answer as 1) S, 2) NS. They say that in order for statement one to be true, every integer between 1 and x, inclusive, must be a factor of x. By testing numbers, this holds true for 1 and 2, but not for 3 and 4. (Page 31 of the number properties guide if anyone cares to look).

Can someone please explain to me why this does not hold true for the numbers 3 and 4. Not sure what I am missing here.

Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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10 Aug 2011, 20:03

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jgonza8 wrote:

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

x is an integer greater than 1. What is the value of x ? 1) There are x unique factors of x. This can happen for 2 only if x>1...because 2 has 2 factors - 1,2 All other values of x do not x unique factors - example - 3 has only 1 unique factors (1,3) other than 3 itself because\(3 = 1*3\) 4 has only 2 unique factors (1,2) other than 4 itself because \(4 = 1*2^2\) 5 has only 1 unique factors (1,5) other than 5 itself because \(5 = 1*5\) 6 has only 3 unique factors (1,2,3) other than 6 itself because \(6 = 1*2*3\) So A/D now 2) The sum of x and any prime number larger than x is odd. Let us substitute...x will only be even value because odd - odd = even 2+5 = 7 4+5 = 9 So multiple values...So B is not sufficient. So A will be the OA

The MGMAT book explains the answer as 1) S, 2) NS. They say that in order for statement one to be true, every integer between 1 and x, inclusive, must be a factor of x. By testing numbers, this holds true for 1 and 2, but not for 3 and 4. (Page 31 of the number properties guide if anyone cares to look).

Can someone please explain to me why this does not hold true for the numbers 3 and 4. Not sure what I am missing here. Have explained above.

Tell if you are not clear. _________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

Last edited by krishp84 on 12 Aug 2011, 18:18, edited 2 times in total.

Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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11 Aug 2011, 22:06

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the question asks what number is equal to the number of his unique factors. 1 has 1 unique factor so 1 is equal to the number of his unique factors. 2 is equal to the number of his unique factors. 3 has only 2 unique factors , 4 and 5 have 2, 11 only 2 and so on.

so the only numbers equal to their unique fators are 1 and 2 . the condition is that x>1 so only 2 applies.

Affiliations: CFA Institute (CFA Candiate), Canadian Institute of Chartered Accountants (CA Candiate), Chartered Alternative Investments Analysts Association (CAIA Candidate)

Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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12 Aug 2011, 18:11

Sovjet wrote:

Why are you guys not considering the number itself as a factor?

To me:

4 has 3 unique factors (not 2) - 1,2,4 5 has 2 unique factors - 1,5 6 has 4 (not 3) unique factors - 1,2,3,6

It doesn't change the answer or anything, but the number itself is a unique factor. They weren't asking for the prime roots.

Yes - This is correct.....I had missed this...

And why does this not affect the answer ? Because Total number of unique factors for any number = 1 + Total number of unique factors other than the number Adding 1 does not affect the count because we are any way comparing the (actual count - 1) However my solution will be wrong if applied for larger numbers say 12 \(12 = 3 *2^2\) Number of unique factors other than \(1 = (1+1)*(2+1) - 1 = 2*3 - 1 = 5\)

You can also calculate and confirm this : Factors of 12 - 1,2,3,4,6,12 Factors of 12 other than 1 = 2,3,4,6,12 All are unique Total number of such unique factors other than 1 = 5

So - Substitute smartly because this is a DATA SUFFICIENCY and NOT PROBLEM SOLVING question. I am editing my post to correct this .... _________________

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

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19 Sep 2013, 14:37

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(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.

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