If x and y are prime numbers, which of the following CANNOT

Question

If x and y are prime numbers, which of the following CANNOT be the sum of x and y?

A) 5
B) 9
C) 13
D) 16
E) 23

Bunuel · Accepted Answer

All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.

Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.

Answer: E.

MSoS · Answer

2 is the only even prime number --> First 4 choices might be possible
23 may only be possible if 23 - 2 (X or Y) = 21 (X or Y) and 21 is prime --> as 21 is not prime, E is the answer

pappueshwar · Answer

hi all,

just thinking aloud,

why is D incorrect? 16 can be written as 14+ 2 ; where 14 is NOT prime number and 2 is a prime number.

AbeinOhio · Answer

Hi,

D is incorrect because 16 = 11 + 5 (so it is possible that 16 can be the sum of 2 prime numbers)

PareshGmat · Answer

Actually, they are asking about both x & y are prime numbers... 14 is out of question for consideration

EMPOWERgmatRichC · Answer

Hi All,

Since the answer choices are all relatively small, this question can be solved with 'brute force' - we just need to find the 4 answers that COULD be the sum of X and Y - the one that's left will be the correct answer.

We're told that X and Y are PRIME NUMBERS... When taking X+Y, can you get to 4 of the 5 answer choices...

A) 5 --> with 2 and 3
B) 9 --> with 2 and 7
C) 13 --> with 2 and 11
D) 16 --> with 3 and 13

Since we've eliminated those 4 options, there's only one answer left...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

VictoryVictoria · Answer

Hi all,

I chose the wrong answer A because I was not paying attention.

This is akin to the except questions in Verbal section, that while one finishes calculation and see an answer.

Hope the GMATClub community can learn from my experience.

EMPOWERgmatRichC · Answer

Hi VictoryVictoria,

Making little mistakes during your studies is not a 'bad' thing - it's a part of the training process (and you can learn from the little mistakes and improve over time). Most silly/little mistakes occur because of a lack of proper note-taking. Doing work "in your head" is the WORST way to approach a GMAT question, so you should never choose to work in that way. By extension, it often helps to summarize the question that is asked - and write that on your pad - so that you have a constant reminder of what you're actually trying to figure out.

When I approached this prompt the first time, the first things I wrote on my pad were:

"X, Y = PRIMES" and "(X+Y) CANNOT be ?"

With just a couple of seconds of note-taking, I have the given information, and the question that is asked, on my pad and I'm ready to get to work.

GMAT assassins aren't born, they're made,
Rich

gmatcafe · Answer

If x and y are prime numbers, which of the following CANNOT be the sum of x and y?

A) 5=2+3
B) 9=2+7
C) 13=2+11
D) 16=5+11
E) 23 - Correct

Sap2002 · Answer

cause we can add 11+5 where both are primes so ...

If x and y are prime numbers, which of the following CANNOT

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GMAT Problem Solving (PS) Questions

If x and y are prime numbers, which of the following CANNOT

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