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Which of the following numbers is not a sum of two prime numbers?

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Joined: 29 Aug 2012
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Which of the following numbers is not a sum of two prime numbers? [#permalink]

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Which of the following numbers is not a sum of two prime numbers?
(A) 78
(B) 88
(C) 51
(D) 60
(E) 10
[Reveal] Spoiler: OA

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Kudos [?]: 1458 [0], given: 270

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Posts: 4426

Kudos [?]: 8453 [1], given: 102

Re: Which of the following numbers is not a sum of two prime numbers? [#permalink]

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New post 08 Aug 2017, 14:03
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Gnpth wrote:
Which of the following numbers is not a sum of two prime numbers?
(A) 78
(B) 88
(C) 51
(D) 60
(E) 10

Dear Gnpth

I'm happy to respond. :-)

I don't know the source, but the question about which you are asking is suspiciously like the question below.
https://gmatclub.com/forum/which-of-the ... 09581.html

Of course, 2 is the only even prime number and the rest are odd. We know that (odd) + (odd) = (even), so all the even numbers could the sum of any two even primes. The one odd number could be the sum of two primes if 2 were one of the two addends. Unfortunately, 49 is not prime, so we cannot write 51 as the sum of two prime numbers. OA = (C)

You don't have to do these calculations, but for the record:
10 = 3 + 7 = 5 + 5
60 = 53 + 7 = 47 + 13
78 = 71 + 7 = 59 + 19
88 = 83 + 5 = 59 + 29
Each other can be written as the sum of two primes in at least two ways.

Does all this make sense?
Mike :-)
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Magoosh Test Prep

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Kudos [?]: 8453 [1], given: 102

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Kudos [?]: 1954 [2], given: 6

Re: Which of the following numbers is not a sum of two prime numbers? [#permalink]

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New post 08 Aug 2017, 14:06
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If we add two whole numbers and get an odd result, we must be adding one even and one odd number.

Since 2 is the only even prime, for an odd number to be the sum of two primes, it would need to be equal to 2 + an odd prime. Since 51 = 2 + 49, and 49 is not prime, we can't write 51 as the sum of two primes.

There is a famous unsolved problem in math known as 'Goldbach's Conjecture', that hypothesizes that every even integer (greater than 2) can be written as the sum of two primes. That's true for every even number anyone has ever tested, but no one has proven if it's true for all even numbers. But it's certainly true for any small even number, including the four even numbers in the answer choices here.
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Kudos [?]: 1954 [2], given: 6

Re: Which of the following numbers is not a sum of two prime numbers?   [#permalink] 08 Aug 2017, 14:06
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Which of the following numbers is not a sum of two prime numbers?

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