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 Post subject: GMAT Number Theory
PostPosted: Tue Apr 09, 2013 11:14 am 
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Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
A. 1
B. 2
C. 3
D. 5
E. 7

(C) We are told that Q is a set of four distinct prime numbers, and the sum of the numbers in Q is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.

If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of Q must be odd to yield an even sum.

Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).

Note: 1 is not a prime number.
----------
In the question, an inner relation between numbers in the set Q (i.e. "Q represents a set of four consecutive prime numbers"). Therefore, 1 might belong to Q. Example: {1,3,5,7}.


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 Post subject: Re: GMAT Number Theory
PostPosted: Tue Apr 09, 2013 11:16 am 
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Quote:
Therefore, 1 might belong to Q. Example: {1,3,5,7}.
1 CAN NOT be an element of Q, because 1 is NOT a prime number, while any element of Q must be a prime number.

Quote:
In the question, an inner relation between numbers in the set Q (i.e. "Q represents a set of four consecutive prime numbers").
Prime numbers in the set are NOT necessarily consecutive, e.g. Q can be {3, 11, 17, 19}.


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 Post subject: Re: GMAT Number Theory
PostPosted: Tue Apr 09, 2013 11:16 am 
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If 1 is a prime no, then 1 will be the answer


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 Post subject: Re: GMAT Number Theory
PostPosted: Tue Apr 09, 2013 11:17 am 
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dave wrote:
If 1 is a prime no, then 1 will be the answer
1 is NOT a prime number.

Prime number is a positive integer, greater than 1, which has no other positive divisors, except 1 and itself.


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