Problem Solving

BTGmoderatorDC wrote: ↑

Thu Jun 25, 2020 6:07 pm

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

Note that except 2, all prime numbers are odd. So, we can draw two conclusions.

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 time-consuming 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
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