Which of the following CANNOT be the sum of two prime numbers?
A) 31
B) 38
C) 33
D) 36
E) 53
OA E
Source: Manhattan Prep
Which of the following CANNOT be the sum of two prime numbers?
This topic has expert replies

 Moderator
 Posts: 5689
 Joined: 07 Sep 2017
 Followed by:18 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 3008
 Joined: 22 Aug 2016
 Location: Grand Central / New York
 Thanked: 470 times
 Followed by:32 members
Note that except 2, all prime numbers are odd. So, we can draw two conclusions.BTGmoderatorDC wrote: ↑Thu Jun 25, 2020 6:07 pmWhich of the following CANNOT be the sum of two prime numbers?
A) 31
B) 38
C) 33
D) 36
E) 53
OA E
Source: Manhattan Prep
1. If the sum of two prime numbers is odd, then one of the prime numbers must be 2.
2. If the sum of two prime numbers is even, then both the prime numbers must be odd.
Let's see each option one by one.
A) 31:
A sum of 31 is possible. We see that 31 = 2 + 29, both prime. Not the correct answer.
B) 38:
It will timeconsuming to find out that 38 is the sum of which two prime numbers. A better approach would be to focus on the odd sum as for the sum to be odd, one of the prime numbers must be 2. This way, we can surely deduce which is the other prime number, other than 2.
C) 33:
A sum of 33 is possible. We see that 33 = 2 + 31, both prime. Not the correct answer.
D) 36:
Ignore this as of now.
E) 53:
A sum of 53 is not possible. We see that 53 = 2 + 51. Note that 51 is not a prime number. The correct answer.
Correct answer: E
Hope this helps!
Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan LSAT  SAT Practice Questions  GMAT Practice Test  GRE Info  and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 6229
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:24 members
Solution:BTGmoderatorDC wrote: ↑Thu Jun 25, 2020 6:07 pmWhich of the following CANNOT be the sum of two prime numbers?
A) 31
B) 38
C) 33
D) 36
E) 53
OA E
Recall that odd + odd = even and odd + even = odd. Also recall that 2 is the only even prime number. If the sum of two distinct prime numbers is odd, then one of them must be 2 since the other one will be odd, and the sum of 2 and an odd number is odd. So let’s check the answer choices that are odd numbers first.
A) 31
31 = 2 + 29
Since 29 is prime, A is not the correct choice.
C) 33
33 = 2 + 31
Since 31 is prime, C is not the correct choice either.
E) 53
53 = 2 + 51
Since 51 is not a prime, E is the correct choice.
Answer: E
Scott WoodburyStewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews