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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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05 Jul 2021, 06:51
05 Jul 2021, 06:51
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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
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If the sum of two prime numbers x and y is odd, then the product of x
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05 Jul 2021, 07:20
05 Jul 2021, 07:20
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Carcass 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
(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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Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
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WE:Education (Education)
Re: If the sum of two prime numbers x and y is odd, then the product of x
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05 Jul 2021, 11:19
05 Jul 2021, 11:19
1
Carcass 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
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8
Remember: 2 is the smallest and ONLY even prime
If x + y = odd, then one of the number has to be 2
otherwise, odd + odd = even
Therefore, xy = even and an even number is always divisible by 2
Hence, option A
