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# If the sum of two prime numbers x and y is odd, then the product of x

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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Updated on: 05 Jul 2019, 02:50
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Question Stats:

92% (00:38) correct 8% (00:48) wrong based on 122 sessions

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If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by

(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

Source: Nova GMAT
Difficulty Level: 500

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Originally posted by Bunuel on 15 Jun 2017, 06:35.
Last edited by SajjadAhmad on 05 Jul 2019, 02:50, edited 1 time in total.
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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15 Jun 2017, 06:45
Bunuel wrote:
If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by

(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

Sum of 2 numbers would be odd only when even number is added to odd number. (Even + Odd = Odd)
Only even prime number is 2. Hence one of the prime numbers must be 2.
Hence the product of x and y must be divisible by 2. Answer A.
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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15 Jun 2017, 07:35
Bunuel wrote:
If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by

(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

Properties of Prime numbers required for solving this question -

1. All Prime numbers (except 2 ) are ODD
2. Sum of 2 prime numbers (except 2) is always Even

Quote:
If the sum of two prime numbers x and y is odd,

Suggests that either x or y is 2 and the product is even.

Quote:
then the product of x and y must be divisible by

Thus, the product must be divisible by 2 , answer will be (A)
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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21 Jun 2017, 00:12
All prime numbers except 2 are odd, hence for the sum of two prime numbers to be odd - one has to be even and hence 2, as 2 is the only even prime number
hence IMO 2 (A) is the OA
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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06 Jul 2017, 16:26
Bunuel wrote:
If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by

(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

All prime numbers are odd, except for 2. Recall that odd + odd = even and that even + odd = odd. If the sum of two prime numbers is odd, then we see that one of the numbers must be 2 and the other number must be odd. Thus, the product xy is a multiple of 2 and must be divisible by 2.

Answer: A
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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08 Jul 2017, 07:36
Why can not be alternative b, since 2x3=6:3=2?
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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08 Jul 2017, 07:41
1
guilherme28 wrote:
Why can not be alternative b, since 2x3=6:3=2?

The question ask xy MUST be divisible by which one of the following numbers, not COULD be divisible by which one of the following numbers. It COULD be divisible by any prime but it MUST be divisible only by 2. So, it will ALWAYS be divisible by 2, and will be divisible by 3 if and only one of the primes is 3.
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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08 Jul 2017, 08:25
Bunuel wrote:
guilherme28 wrote:
Why can not be alternative b, since 2x3=6:3=2?

The question ask xy MUST be divisible by which one of the following numbers, not COULD be divisible by which one of the following numbers. It COULD be divisible by any prime but it MUST be divisible only by 2. So, it will ALWAYS be divisible by 2, and will be divisible by 3 if and only one of the primes is 3.

Oh, that's right! What a dumb question of mine! Thanks a lot.
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Re: If the sum of two prime numbers x and y is odd, then the product of x  [#permalink]

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08 May 2018, 07:21
Top Contributor
Bunuel wrote:
If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by

(A) 2
(B) 3
(C) 4
(D) 5
(E) 8

Some important rules:
1. ODD + ODD = EVEN
2. ODD + EVEN = ODD
3. EVEN + EVEN = EVEN

4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN

If x + y = ODD, then one of the values must be ODD and the other value must be EVEN
Since 2 is the ONLY EVEN prime number, then we can be certain that either x or y equals 2.
So, xy = (2)(some ODD prime number)
In other words, xy = (EVEN )(ODD) = EVEN (from rule 5)
So, xy is EVEN, which means xy is divisible by 2
Answer: A

Cheers,
Brent
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Re: If the sum of two prime numbers x and y is odd, then the product of x   [#permalink] 08 May 2018, 07:21
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# If the sum of two prime numbers x and y is odd, then the product of x

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