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

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Manager
Joined: 07 Jun 2017
Posts: 176
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Positive integers x and y leave remainders 5 and 8 respectively when [#permalink]

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24 Oct 2017, 01:05
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63% (01:52) correct 38% (01:23) wrong based on 64 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
[Reveal] Spoiler: OA

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email: nkmungila@gmail.com
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Manager
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Posts: 239
GPA: 3.57
Re: Positive integers x and y leave remainders 5 and 8 respectively when [#permalink]

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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   [#permalink] 24 Oct 2017, 01:15
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# Positive integers x and y leave remainders 5 and 8 respectively when

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