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Manager  G
Joined: 04 Jun 2020
Posts: 112
Location: India
Concentration: Strategy, General Management
GPA: 3.4
WE: Engineering (Consulting)
Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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3 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:32) correct 32% (01:27) wrong based on 69 sessions

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Which of the following CANNOT be the sum of two prime numbers?

A) 31
B) 38
C) 33
D) 36
E) 53
Director  G
Joined: 16 Feb 2015
Posts: 657
Location: United States
Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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1
Explanation:

A. 29 + 2
B. 31 + 7
C. 31 + 2
D. 31 + 5
E. 53 is prime only

IMO-E
Manager  B
Joined: 11 Oct 2019
Posts: 103
Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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A) 31 = 29 + 2
B) 38 = 31 + 7
C) 33 = 31 + 2
D) 36 = 29 + 7
E) Can not be the sum of two prime numbers
Manager  S
Joined: 05 Oct 2014
Posts: 54
Concentration: Technology, Entrepreneurship
Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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3
In the options , there are 3 odd numbers and 2 even numbers given.

Odd+ Even = Odd
As there is only 1 prime number which is even i.e. 2
First, we need to check odd numbers in options :

31 = 29 + 2 (possible)
33 = 31 + 2 (possible)
53 = 51 + 2 ( not possible as 51 is not prime)

GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2395
Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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2
There's a famous conjecture in Number Theory known as "Goldbach's Conjecture", which is true for every number anyone has looked at, but remains unproven for enormous numbers. That conjecture says "every even number greater than 2 can be written as a sum of two primes". So if you know in advance that's true for all the small even numbers, you can be certain this question has an odd answer.

If we can write an odd number as the sum of two primes, we need to use the prime 2, the only even prime, because it's only by adding an even and an odd that you get an odd sum. So to answer this question, we just need to find an answer that is not equal to 2 + p, where p is an odd prime, and 53 is right, because 51 is not prime (51 = 3*17).
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Re: Which of the following CANNOT be the sum of two prime numbers?   [#permalink] 02 Jul 2020, 07:19

# Which of the following CANNOT be the sum of two prime numbers?   