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Difficulty:
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Question Stats:
57% (01:34) correct
43%
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wrong
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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.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.
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.
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.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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.
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.
Answer is A.
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.
Answer is A.
l0rrie
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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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!
IanStewart
Expert
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 10 Sep 2026
Posts: 4,146
Location: United States
GMAT 1: 780 Q51 V47
Expert reply
GMAT 1: 780 Q51 V47
Posts: 4,146
Silver89
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.
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ianstewartgmat.com
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Posts: 101
IMO the answer has to be A
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
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 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.
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.
jgonza8
Tell if you are not clear.
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.
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.
Sovjet
Joined: 21 Jun 2011
Last visit: 23 May 2012
Posts: 17
Affiliations: CFA Institute (CFA Candiate), Canadian Institute of Chartered Accountants (CA Candiate), Chartered Alternative Investments Analysts Association (CAIA Candidate)
Location: Canada
Concentration: Finance, International Business
WE:Research (Finance: Investment Banking)
Posts: 17
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.
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.
Sovjet
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 ....
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.
Answer: A.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
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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.
Answer: A.
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
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