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# If the average (arithmetic mean) of positive integers x and y is a pos

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
If the average (arithmetic mean) of positive integers x and y is a pos  [#permalink]

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08 Jan 2018, 23:40
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75% (hard)

Question Stats:

49% (01:48) correct 51% (01:53) wrong based on 81 sessions

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If the average (arithmetic mean) of positive integers x and y is a positive integer, is it prime?

(1) The average (arithmetic mean) of 3x and 3y is 12.
(2) The sum of x and y is divisible by 4.

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Re: If the average (arithmetic mean) of positive integers x and y is a pos  [#permalink]

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09 Jan 2018, 04:11
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Bunuel wrote:
If the average (arithmetic mean) of positive integers x and y is a positive integer, is it prime?

(1) The average (arithmetic mean) of 3x and 3y is 12.
(2) The sum of x and y is divisible by 4.

Average of x and y = (x+y)/2 = z (say, where z is a positive integer). We have to answer whether z is prime or not.

(1) Given, (3x + 3y)/2 = 12 or 3x + 3y = 24 or (x+y) = 8. So we can find z, so we will be able to decipher whether z is prime or not. Sufficient.

(2) Sum of x+y could be 4 or 8 or 12 or 16 etc...
So z could be 2 or 4 or 6 etc.. so it could be prime (2) or it might not be (4, 6 etc). So Insufficient.

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Joined: 29 Aug 2017
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Re: If the average (arithmetic mean) of positive integers x and y is a pos  [#permalink]

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11 Feb 2018, 04:28
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Bunuel wrote:
If the average (arithmetic mean) of positive integers x and y is a positive integer, is it prime?

(1) The average (arithmetic mean) of 3x and 3y is 12.
(2) The sum of x and y is divisible by 4.

Hey Shouldn't the answer be A, Please confirm- as option B) has two possibilities (2-which is prime) and 4,6,8(non-primes)
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Joined: 02 Sep 2009
Posts: 50009
Re: If the average (arithmetic mean) of positive integers x and y is a pos  [#permalink]

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11 Feb 2018, 08:21
PearlRay wrote:
Bunuel wrote:
If the average (arithmetic mean) of positive integers x and y is a positive integer, is it prime?

(1) The average (arithmetic mean) of 3x and 3y is 12.
(2) The sum of x and y is divisible by 4.

Hey Shouldn't the answer be A, Please confirm- as option B) has two possibilities (2-which is prime) and 4,6,8(non-primes)

Yes, the answer is A, not D. Edited. Thank you.
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Re: If the average (arithmetic mean) of positive integers x and y is a pos &nbs [#permalink] 11 Feb 2018, 08:21
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# If the average (arithmetic mean) of positive integers x and y is a pos

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