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If a and b are prime numbers, which of the following CANNO

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If a and b are prime numbers, which of the following CANNO [#permalink]

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If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

A. 19
B. 25
C. 33
D. 46
E. 53
[Reveal] Spoiler: OA

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Re: If a and b are prime numbers, which of the following CANNO [#permalink]

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New post 12 Mar 2013, 00:41
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emmak wrote:
If a and b are prime numbers, which of the following CANNOT be the sum of a and b?
a) 19
b) 25
c) 33
d) 46
e) 53


If we subtract 2 from each of the first three options, we see that it gives a prime number.

19-2 = 17

25-2 = 23

33-2 = 31

Now 46-3 = 43.

Thus the only number left is 53.

E.
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Re: If a and b are prime numbers, which of the following CANNO [#permalink]

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New post 12 Mar 2013, 06:32
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emmak wrote:
If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

A. 19
B. 25
C. 33
D. 46
E. 53


All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.

Now, 53=2+51. Since 51 is not a prime (51=3*17) then 53 cannot be written as the sum of two prime numbers.

Answer: E.

Similar question: if-x-and-y-are-prime-numbers-which-of-the-following-cannot-127129.html

Hope it helps.
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Re: If a and b are prime numbers, which of the following CANNO [#permalink]

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New post 12 Mar 2013, 07:01
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Prime numbers are a fundamental part in the GMAT, so having questions such as these are a real blessing. Thanks emmak (you've earned a Kudos from me).

I'll kick this off by stating which concepts are going to be useful in solving this problem :

1/ Addition laws : ODD + EVEN = ODD, ODD + ODD = EVEN
2/ All prime numbers except 2 are ODD !!!
3/ Prime number list up until 31
(Yeah, it's harsh, but you need to know your prime numbers, otherwise, you'll be missing out on a lot of shortcuts)

Now, let's consider the answer choices.

You'll notice that all the answer choices except D are odd. So there's got to be a 2 in the mix (if the question stem is correct) so :

A/ 19 = 2 + 17 (17 is prime, so cross off A) ;
B/ 25 = 2 + 23 (23 is prime, so cross off B) ;
C/ 33 = 2 + 31 (31 is prime, so cross off C) ;
D/ 46 = 23 + 23 (23 is prime, so cross off D);

This leaves us with answer choice E. And incidentally 51 IS a prime number. ;)

An alternative to this method is to use the list of prime numbers up to 31 and make combinations. Depending on how comfortable you are with numbers, this can be a time-saver or a time-consuming method. So use at your own risk.

Hope that helped :-D

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If a and b are prime numbers, which of the following CANNOT be the sum [#permalink]

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New post 05 Jul 2015, 15:28
If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

a) 19
b) 25
c) 33
d) 46
E) 53
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Re: If a and b are prime numbers, which of the following CANNOT be the sum [#permalink]

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New post 05 Jul 2015, 15:32
sunita123 wrote:
If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

a) 19
b) 25
c) 33
d) 46
E) 53


Please search for a question before you post. The same question has been discussed at if-a-and-b-are-prime-numbers-which-of-the-following-canno-149049.html?fl=similar

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Re: If a and b are prime numbers, which of the following CANNO [#permalink]

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Re: If a and b are prime numbers, which of the following CANNO [#permalink]

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New post 10 Aug 2017, 21:28
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Re: If a and b are prime numbers, which of the following CANNO   [#permalink] 10 Aug 2017, 21:28
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