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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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New post 11 Mar 2013, 23:32
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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

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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, 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, 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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New post 05 Jul 2015, 15:44
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Re: If a and b are prime numbers, which of the following CANNO  [#permalink]

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New post 02 Oct 2018, 11:19
Quote:
In order for the sum of two integers to be odd, one of the numbers must be even. The only even prime number is 2. Therefore, if the sum of two prime numbers is odd, one of the numbers must be 2.


(A) 19 (odd) = 2 + 17

(B) 25 (odd) = 2 + 23

(C) 33 (odd) = 2 + 31

(D) 46 (even) = 3 + 43

(E) 53 (odd) = 2 + 51 (51 is not prime)

51 is not prime, so the correct answer is 53, answer choice E.

Quote:
Important: 51 is often used as a trap answer on prime number questions. 51 is a multiple of 3, and therefore not prime. You can check this using the divisibility rule for 3, as the sum of the digits (5+1 = 6) is a multiple of 3.

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Re: If a and b are prime numbers, which of the following CANNO   [#permalink] 02 Oct 2018, 11:19
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