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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 63% (01:01) correct 37% (00:53) wrong based on 297 sessions

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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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Math Expert V
Joined: 02 Sep 2009
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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).

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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).

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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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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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!!
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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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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.

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?

Thanks,
Alok322
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Math Expert V
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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.

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?

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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I think this is a poor-quality 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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I think this is a poor-quality 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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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 = 2x-4 = -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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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.

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?

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).

Thanks.
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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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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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Good one! I did not think about a number being a multiple of itself
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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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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?
Math Expert V
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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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I think this is a high-quality 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?
Math Expert V
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subhash2688 wrote:
I think this is a high-quality 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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