a and b are prime numbers

[jain2016]

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

OAE

Hi Experts ,

Please explain.


Thanks ,

SJ

[[email protected]]

Hi jain2016,

This question requires a knowledge of PRIME numbers and a bit of 'brute force' to solve. We're looking for an answer that CANNOT be the sum of two prime numbers, so we could prove that 4 of the answers CAN be the sum of two prime numbers (so that we can eliminate those 4 answers):

A) 19 = 2 + 17
B) 25 = 2 + 23
C) 33 = 2 + 31
D) 46 = 3 + 43

Since those answers all CAN be the sum of two primes, there's only one answer left...

Final Answer: E

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

[Brent@GMATPrepNow]

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

The GMAT LOVES testing whether or not people recognize that 2 is prime (many people believe 2 isn't prime because it's even).

Notice that only 1 of the answer choices is even (D). This is the trap answer for people who believe that ALL prime numbers are odd. These people will look at the other answer choices (which are all odd) and think "hmmm, the only way for 2 integers to add to a odd number is for 1 number to be odd and 1 number to be even. People who believe that all prime numbers are odd will automatically eliminate A, B, C and E and choose D.

As Rich has shown, A, B, C and D can all be rewritten as the sum of 2 primes. So, the answer is E

Cheers,
Brent

[Matt@VeritasPrep]

Another clue here: the only way to get an odd sum when summing two integers is to have Even + Odd. Since four of the answers are odd, and at least three of them MUST be possible, we know that the even number to test must be an even prime, or 2. Working from there

19 = 17 + 2
25 = 23 + 2
33 = 31 + 2

so those are all possible. Trying the next prime (3), we find

46 = 43 + 3

and we're set! Since all four of these can be represented as the sum of two primes, by elimination E must be the right answer.

[Jeff@TargetTestPrep]

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

Since 2 + 17 = 19, A is not the answer.

Since 23 + 2 = 25, B is not the answer.

Since 31 + 2 = 33, C is not the answer.

Since 43 + 3 = 46, D is not the answer.

Thus, the answer is E.

Alternate Solution:

We see that all but one of the answer choices are odd numbers. Since the only even prime is 2, the only way the sum of two prime numbers is odd is if one of the numbers is 2. We can subtract 2 from the odd answer choices and see if we get a composite (i.e., non-prime) number:

Since 19 - 2 = 17 is prime, A is not the answer.

Since 25 - 2 = 23 is prime, B is not the answer.

Since 33 - 2 = 31 is prime, C is not the answer.

Since 53 - 2 = 51 is not prime, there is no way 53 is the sum of two prime numbers. Since we already found the answer, we don't even need to test the answer choice that is an even number.

Answer: E