If a and b are prime numbers, which of the following CANNO

Prime numbers are a fundamental part in the GMAT, so having questions such as these are a real blessing. Thanks emmak (you've earned a Kudos from me).

I'll kick this off by stating which concepts are going to be useful in solving this problem :

1/ Addition laws : ODD + EVEN = ODD, ODD + ODD = EVEN
2/ All prime numbers except 2 are ODD !!!
3/ Prime number list up until 31 (Yeah, it's harsh, but you need to know your prime numbers, otherwise, you'll be missing out on a lot of shortcuts)

Now, let's consider the answer choices.

You'll notice that all the answer choices except D are odd. So there's got to be a 2 in the mix (if the question stem is correct) so :

A/ 19 = 2 + 17 (17 is prime, so cross off A) ;
B/ 25 = 2 + 23 (23 is prime, so cross off B) ;
C/ 33 = 2 + 31 (31 is prime, so cross off C) ;
D/ 46 = 23 + 23 (23 is prime, so cross off D);

This leaves us with answer choice E. And incidentally 51 IS a prime number.

An alternative to this method is to use the list of prime numbers up to 31 and make combinations. Depending on how comfortable you are with numbers, this can be a time-saver or a time-consuming method. So use at your own risk.

Hope that helped

If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

a) 19
b) 25
c) 33
d) 46
E) 53

Please search for a question before you post. The same question has been discussed at if-a-and-b-are-prime-numbers-which-of-the-following-canno-149049.html?fl=similar

Merging topics.

Please refer to the discussion above.

(A) 19 (odd) = 2 + 17

(B) 25 (odd) = 2 + 23

(C) 33 (odd) = 2 + 31

(D) 46 (even) = 3 + 43

(E) 53 (odd) = 2 + 51 (51 is not prime)

51 is not prime, so the correct answer is 53, answer choice E.

Eliminate the answer choices by proving the possibility that an answer choice is a summation of prime numbers as follows:

A) 19 - 2 = 17 - Possible sum since 2 and 17 are prime
B) 25 - 2 = 23 - Possible (23 is a prime number)
C) 33 - 2 = 31 - Possible ( 31 is a prime number)
D) 46 -2 = 44 - 44 not a prime number. subtracting 3, 46 - 3 = 43, 43 and 3 are prime numbers
E) 53 - correct choice