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

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Math Expert
Joined: 02 Sep 2009
Posts: 62353
If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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02 Nov 2016, 01:46
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Question Stats:

92% (01:48) correct 8% (01:48) wrong based on 85 sessions

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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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Joined: 06 Jun 2016
Posts: 250
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
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GPA: 3.9
Re: If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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02 Nov 2016, 02:23
1
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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If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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02 Nov 2016, 08:08
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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Re: If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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02 Nov 2016, 08:26
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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If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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08 Dec 2017, 10:03
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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Posts: 14448
Re: If x and y are positive integers that have remainders of 2 and 5, resp  [#permalink]

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06 Jan 2020, 07:27
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Re: If x and y are positive integers that have remainders of 2 and 5, resp   [#permalink] 06 Jan 2020, 07:27
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