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Can the positive integer q be written as the sum of three different

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Can the positive integer q be written as the sum of three different [#permalink]

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New post 10 Dec 2017, 00:22
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Kudos [?]: 139308 [0], given: 12783

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Re: Can the positive integer q be written as the sum of three different [#permalink]

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New post 10 Dec 2017, 00:24
Bunuel wrote:
Can the positive integer q be written as the sum of three different positive prime numbers?

(1) q is less than 11.
(2) q is odd.


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https://gmatclub.com/forum/can-the-posi ... 67422.html (OG)
https://gmatclub.com/forum/if-n-is-a-po ... 65942.html (Kaplan)
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Re: Can the positive integer q be written as the sum of three different [#permalink]

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New post 10 Dec 2017, 04:11
Bunuel wrote:
Can the positive integer q be written as the sum of three different positive prime numbers?

(1) q is less than 11.
(2) q is odd.


Primes list {2,3,5,7,11...}

(1) q is less than 11. Then q = {2,3,5} = 10 < 11 = sum of three different primes; or, q = {2,3,"4"} = not all primes, not suf.
(2) q is odd. Then q = odd = {3,5,7} = sum of three different primes; so "yes it can"; or, q = odd = {5,7,"9"} = not all primes, not suf.
(3) q = odd < 11. The smallest possible sum of three different primes < 11 is {2,3,5} = 10 which is not an odd, so sufficient.

(C) is the answer.

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Re: Can the positive integer q be written as the sum of three different   [#permalink] 10 Dec 2017, 04:11
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