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Master | Next Rank: 500 Posts
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by grandh01 » Thu Aug 23, 2012 3:07 pm
If the sum of a set of ten different
positive prime numbers is an even
number, which of the following prime
numbers CANNOT be in the set ?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11

OA is A
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by Brent@GMATPrepNow » Thu Aug 23, 2012 3:41 pm
grandh01 wrote:If the sum of a set of ten different
positive prime numbers is an even
number, which of the following prime
numbers CANNOT be in the set ?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11

OA is A
First recognize that there is only 1 prime number that is even (this concept is often tested on the GMAT).

If the 10 numbers are all different, then there are only 2 possible cases:

case a) the number 2 (even), plus 9 odd prime numbers
case b) 10 odd prime numbers

In case a, the sum of the 10 numbers will be odd
In case b, the sum of the 10 numbers will be even

Since we're told that the sum is even, we can eliminate case a, which means all 10 numbers are odd.
If all 10 numbers are odd, then 2 cannot be one of the numbers.

So, the answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by coolhabhi » Thu Aug 23, 2012 9:02 pm
grandh01 wrote:If the sum of a set of ten different
positive prime numbers is an even
number, which of the following prime
numbers CANNOT be in the set ?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11

OA is A
All prime numbes are odd except for 2 which is the only even prime.

So for the sum of a set of ten different positive prime numbers to be an even number all the ten numbers should be odd primes.
A Small example : 3 + 5 = 8 (Even)

If there is one even prime and 9 odd primes then the sum of 9 odd primes will be odd and when the one even prime is added the sum would be a odd number.
Example : 2+3+5+7 = 17 (Odd) (3+5+7 = 15)

So Answer 2.
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by vk_vinayak » Thu Aug 23, 2012 10:18 pm
grandh01 wrote:If the sum of a set of ten different
positive prime numbers is an even
number, which of the following prime
numbers CANNOT be in the set ?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11

OA is A
Question tests ODD and EVEN concept. Note that only one of the option is EVEN. Pick A.
- VK

I will (Learn. Recognize. Apply)
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by SmartAssJun » Fri Aug 24, 2012 4:51 am
grandh01 wrote:If the sum of a set of ten different
positive prime numbers is an even
number, which of the following prime
numbers CANNOT be in the set ?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11

OA is A
There's only 1 prime number that happens to be an even number, which is the number 2.
So you can't possibly get two or more prime numbers that are both primes in the set.
And there's ten prime numbers in the number set, if you included the number 2 in the set, the sum of the other nine prime numbers would definitely be an odd number.
So the number 2 is out.
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