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Positive integers x and y leave remainders 5 and 8 respectively when

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Joined: 07 Jun 2017
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Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
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Positive integers x and y leave remainders 5 and 8 respectively when  [#permalink]

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New post 24 Oct 2017, 01:05
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A
B
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Difficulty:

  55% (hard)

Question Stats:

62% (01:48) correct 38% (01:28) wrong based on 73 sessions

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Positive integers x and y leave remainders 5 and 8 respectively when divided by 11. Which of the following is not a possible value of x + 2y?

A. 120
B. 196
C. 219
D. 351
E. 560

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Re: Positive integers x and y leave remainders 5 and 8 respectively when  [#permalink]

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New post 24 Oct 2017, 01:15
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nkmungila wrote:
Positive integers x and y leave remainders 5 and 8 respectively when divided by 11. Which of the following is not a possible value of x + 2y?

A. 120
B. 196
C. 219
D. 351
E. 560


It should be B

We can rewrite both x and y as

\(x = 11m + 5\)
\(y = 11p + 8\)

where m and n are non negative integers.

\(x + 2y = 11m + 5 + 2 (11p +8)\)
\(x + 2y = 11m + 22p + 5 + 16\)
\(x + 2y = 11m + 22p + 21\)

We can now rewrite it as

\(x + 2y = 11m + 22p + 11 + 10\)

First 3 terms are multiples of 11 and an additional 10. So this expression results in a number that is 10 more than a multiple of 11. In other words, dividing the number would result in a remainder of 10. Now looking at options.

A. \(120 = 11*10 + 10\)
B. \(196 = 11*17 + 9\)
C. \(219 = 11*19 + 10\)
D. \(351 = 11*31 + 10\)
E. \(560 = 11*50 + 10\)
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Re: Positive integers x and y leave remainders 5 and 8 respectively when &nbs [#permalink] 24 Oct 2017, 01:15
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