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If x and y are positive integers that have remainders of 2 and 5, resp

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Bunuel
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If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   02 Nov 2016, 02:46
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If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?

A. 16
B. 19
C. 40
D. 49
E. 72
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D
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Vinayak Shenoy
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Re: If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   02 Nov 2016, 03:23
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Bunuel wrote:
If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?

A. 16
B. 19
C. 40
D. 49
E. 72


IMO D
x=7k+2 and y=7q+5 (x+y= 7n+7)
x+y= multiple of 7
only D is multiple of 7.
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Abhishek009
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If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   02 Nov 2016, 09:08
Bunuel wrote:
If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?

A. 16
B. 19
C. 40
D. 49
E. 72


Minimum value of x = 9 and y = 12=>

x + y = 21 ( Divisible by 7 )

So, The correct answer choice will be one that will be divisible by 7..

Among the given options only (D) satisfies, hence answer must be (D)
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stonecold
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Re: If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   02 Nov 2016, 09:26
Abhishek009 wrote:
Bunuel wrote:
If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?

A. 16
B. 19
C. 40
D. 49
E. 72


Minimum value of x = 9 and y = 12=>

x + y = 21 ( Divisible by 7 )

So, The correct answer choice will be one that will be divisible by 7..

Among the given options only (D) satisfies, hence answer must be (D)


Hi..!!
I think you got one part incorrect.
When you say that the minimum value of x and y => 9,12
Actually i think the values will be 2 and 5 respectively.

Am i missing something here?

Regards
Stone Cold
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gracie
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If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   08 Dec 2017, 11:03
Bunuel wrote:
If x and y are positive integers that have remainders of 2 and 5, respectively, when divided by 7, which of the following could be the sum of x and y?

A. 16
B. 19
C. 40
D. 49
E. 72


x=7q+2
y=7p+5
x+y=7q+7p+7➡7(q+p+1)
49 is the only multiple of 7
D
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Re: If x and y are positive integers that have remainders of 2 and 5, resp [#permalink] New post   06 Jan 2020, 08:27
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Re: If x and y are positive integers that have remainders of 2 and 5, resp [#permalink]
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