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If \(x\) is an integer, then is \(x\) a prime number? (1) \(x\) is a multiple of a prime number. (2) \(x\) is a product of two integers.
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16 Sep 2014, 00:16
Official Solution: Statement (1) by itself is not sufficient. Multiples of a prime number are not prime except the prime number itself. For example, 3 is prime and its multiples are 3 itself (prime), 6 (not prime), etc. Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example \(3=1*3\) is prime, but \(6=3*2\) is not prime. Statements (1) and (2) combined are not sufficient. If both statements are combined,\(x\) can still be 3 (prime) or 6 (not prime). Answer: E
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Re: M0126
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25 Feb 2015, 11:23
Bunuel wrote: Official Solution:
Statement (1) by itself is not sufficient. Multiples of a prime number are not prime except the prime number itself. For example, 3 is prime and its multiples are 3 itself (prime), 6 (not prime), etc. Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example \(3=1*3\) is prime, but \(6=3*2\) is not prime. Statements (1) and (2) combined are not sufficient. If both statements are combined,\(x\) can still be 3 (prime) or 6 (not prime).
Answer: E Thanks for the explanation Bunuel. I missed this example because I didn't consider that it is true to say that a number is a multiple of itself. For example, 3 is a multiple of 3.



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Re: M0126
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08 Oct 2015, 03:00
In "(2) x is a product of two integers", I was confused with "x is a product of ANY/ONLY two integers". I presupposed that the author meant "ONLY" so question went wrong. Can you please guide how to interpret such questions?
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Re: M0126
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07 Feb 2016, 05:33
Hi,
in my opinion Statement 1 is sufficient: "(1) x is a multiple of a prime number." As Bunuel wrote, a multiple of 3 is 6. If x is a multiple of a prime number it is itself definitely not a prime number > Sufficient.
Where is the error in my thought? I don't get it...
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Re: M0126
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07 Feb 2016, 06:18
AnikaJu wrote: Hi,
in my opinion Statement 1 is sufficient: "(1) x is a multiple of a prime number." As Bunuel wrote, a multiple of 3 is 6. If x is a multiple of a prime number it is itself definitely not a prime number > Sufficient.
Where is the error in my thought? I don't get it...
Thanks!! Hi, the point which you are missing is the number itself is a multiple.. so 3 is a multiple of 3.. 3*1=3.. that is the reason statement 1 is not suff
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Re: M0126
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20 Sep 2016, 11:29
Bunuel wrote: Official Solution:
Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example \(3=1*3\) is prime, but \(6=3*2\) is not prime.
Answer: E Dear Bunuel, When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers? Please clarify. Thanks, Alok322
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Re: M0126
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21 Sep 2016, 04:07
Alok322 wrote: Bunuel wrote: Official Solution:
Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example \(3=1*3\) is prime, but \(6=3*2\) is not prime.
Answer: E Dear Bunuel, When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers? Please clarify. Thanks, Alok322 x is a product of two integers means that x can be represented as the product of two integers.
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Re M0126
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22 Oct 2016, 06:44
I think this is a poorquality question and I don't agree with the explanation. the question may be misleading since statement 2 can be misunderstood since its vague



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25 Nov 2016, 08:54
I think this is a poorquality question. Statement 2 must include ANY or ONLY. It is ambiguous for a DS question. I don't think GMAC will have an ambiguous question



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Re: M0126
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08 Dec 2016, 17:18
Is x = Prime? 1, If prime 2 , x could be 2,4,6,8.. If prime 3 , x could be 3,6,9,12.. If prime 5 , x could be 5,10,15,... So BCE 2, x = 0x1 =0 ( 0 is not prime) x = 2x4 = 8 ( 8 is not prime) x= 2x1 = 2 ( 2 is prime) So eliminate B Next, If x = 2,5,7 are prime numbers so I have chosen C Pls help me.
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Re: M0126
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07 Jan 2017, 22:52
Bunuel wrote: Alok322 wrote: Bunuel wrote: Official Solution:
Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example \(3=1*3\) is prime, but \(6=3*2\) is not prime.
Answer: E Dear Bunuel, When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers? Please clarify. Thanks, Alok322 x is a product of two integers means that x can be represented as the product of two integers. Hello Bunuel Need a clarification here. I am still confused about the statement 2. Product of TWO integers: 3*1 Product of THREE integers: 1*3*2= 6 (one is a factor of 3 as well) Statement 2 should be sufficient according to the above analysis because ONLY PRIME NUMBERS HAVE TWO FACTORS (ONE AND ITSELF). Please clarify. Thanks.



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Re: M0126
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28 Jun 2017, 10:07
in ALL the books I've read they say that one and zero are unique since they are either primes nor composites
why did you consider 1 as prime here? is that a unique thing in GMAT?
also if you count 1 as a prime wouldn't it make the situation as stated in the previous post in this topic?



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Re: M0126
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28 Jun 2017, 10:11
kamyar94 wrote: in ALL the books I've read they say that one and zero are unique since they are either primes nor composites
why did you consider 1 as prime here? is that a unique thing in GMAT?
also if you count 1 as a prime wouldn't it make the situation as stated in the previous post in this topic? 1 is NOT a prime number and nowhere in the solution it is stated otherwise.
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Re: M0126
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03 Jul 2017, 19:15
Good one! I did not think about a number being a multiple of itself



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Re: M0126
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04 Sep 2017, 11:21
There is no where mentioned the sign of integers. Prime numbers are positive. In absence of this information, answer becomes E.
Is it correct to consider this point?



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Re M0126
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09 Sep 2017, 10:13
I think this the explanation isn't clear enough, please elaborate. Statement 1 leads to the conclusion that x is not prime. Doesn't this mean it's sufficient?



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Re: M0126
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09 Sep 2017, 10:17
shrutip24 wrote: I think this the explanation isn't clear enough, please elaborate. Statement 1 leads to the conclusion that x is not prime. Doesn't this mean it's sufficient? x is a multiple of a prime number does not mean that x is not a prime. For example, 5 is a multiple of 5, so x could be a prime.
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Re M0126
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08 Oct 2017, 21:51
I think this is a highquality question and I don't agree with the explanation. With the statement 1, we can derive that x is not a prime number as its a multiple of a prime number. Why not option 1 is the correct answer?



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Re: M0126
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08 Oct 2017, 21:55
subhash2688 wrote: I think this is a highquality question and I don't agree with the explanation. With the statement 1, we can derive that x is not a prime number as its a multiple of a prime number. Why not option 1 is the correct answer? x is a multiple of a prime number does not mean that x is not a prime. For example, 5 is a multiple of 5, so x could be a prime.
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