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# The integers x and y are both positive, the remainder when x

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Manager
Joined: 01 Sep 2012
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Kudos [?]: 42 [0], given: 19

The integers x and y are both positive, the remainder when x [#permalink]  05 Jan 2013, 13:17
00:00

Difficulty:

55% (hard)

Question Stats:

66% (03:38) correct 34% (01:49) wrong based on 93 sessions
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT

A. 125
B. 101
C. 77
D. 51
E. 41

I got this right but it took me 2 minutes.
I wonder if there is a quick way to solve this question without plugging numbers to X and Y.
I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.
thanks
[Reveal] Spoiler: OA

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If my answer helped, dont forget KUDOS!

IMPOSSIBLE IS NOTHING

Last edited by Bunuel on 07 Jan 2013, 03:29, edited 2 times in total.
Edited the question.
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Kudos [?]: 454 [0], given: 182

Re: The integers x and y are both positive, the remainder when x [#permalink]  05 Jan 2013, 14:24
Your question "Each of the following is a possible value of ??? EXCEPT" seems to be incomplete. Which value is required to be determined?
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PraPon

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Manager
Joined: 01 Sep 2012
Posts: 129
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Kudos [?]: 42 [0], given: 19

Re: The integers x and y are both positive, the remainder when x [#permalink]  05 Jan 2013, 23:59
PraPon wrote:
Your question "Each of the following is a possible value of ??? EXCEPT" seems to be incomplete. Which value is required to be determined?

You are right.
Edited.
2X+Y.
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If my answer helped, dont forget KUDOS!

IMPOSSIBLE IS NOTHING

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Posts: 1422
Location: India
Concentration: Finance, Marketing
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Kudos [?]: 783 [0], given: 62

Re: The integers x and y are both positive, the remainder when x [#permalink]  06 Jan 2013, 00:50
Expert's post
roygush wrote:
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2X+Y EXCEPT:

A)125
B)101
C)77
D)51
E)41

I got this right but it took me 2 minutes.
I wonder if there is a quick way to solve this question without plugging numbers to X and Y.
I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.
thanks

There are two statements in the question:
1) The remainder when x is divided by 12 is 7. This can be written as $$x=12I + 7$$, where I is an integer.
2) The remainder when y is divided by 12 is 3. This can be written as $$y=12J + 3$$, where J is an integer.

One thing to note here is that the maximum remainder that these two equations can generate is 11. So $$2x$$ will not be equal to $$12I+14$$ but will be equal to $$12I+2$$.

Therefore $$2x + y = 12(I+J) + 5$$ or any multiple of 12 + 5.
51 doesn't follows such pattern. Hence is the answer.
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Joined: 02 Sep 2009
Posts: 27465
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Kudos [?]: 42107 [1] , given: 5956

Re: The integers x and y are both positive, the remainder when x [#permalink]  07 Jan 2013, 03:34
1
KUDOS
Expert's post
roygush wrote:
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT

A. 125
B. 101
C. 77
D. 51
E. 41

I got this right but it took me 2 minutes.
I wonder if there is a quick way to solve this question without plugging numbers to X and Y.
I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.
thanks

The remainder when x is divided by 12 is 7: $$x=12q+7$$ --> $$2x=24q+14$$.
The remainder when y is divided by 12 is 3: $$y=12p+3$$.

$$2x+y=(24q+14)+(12p+3)=24q+12p+12+5=12(2q+p+1)+5=(multiple \ of \ 12)+5$$. Only D is not a multiple of 12 plus 5.

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Manager
Joined: 01 Sep 2012
Posts: 129
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Kudos [?]: 42 [0], given: 19

Re: The integers x and y are both positive, the remainder when x [#permalink]  07 Jan 2013, 06:04
Bunuel wrote:
roygush wrote:
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT

A. 125
B. 101
C. 77
D. 51
E. 41

I got this right but it took me 2 minutes.
I wonder if there is a quick way to solve this question without plugging numbers to X and Y.
I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.
thanks

The remainder when x is divided by 12 is 7: $$x=12q+7$$ --> $$2x=24q+14$$.
The remainder when y is divided by 12 is 3: $$y=12p+3$$.

$$2x+y=(24q+14)+(12p+3)=24q+12p+12+5=12(2q+p+1)+5=(multiple \ of \ 12)+5$$. Only D is not a multiple of 12 plus 5.

bunuel, can we apply this method on any remainders problem?
write the two equations and then work from there?
_________________

If my answer helped, dont forget KUDOS!

IMPOSSIBLE IS NOTHING

Math Expert
Joined: 02 Sep 2009
Posts: 27465
Followers: 4305

Kudos [?]: 42107 [0], given: 5956

Re: The integers x and y are both positive, the remainder when x [#permalink]  07 Jan 2013, 08:44
Expert's post
roygush wrote:
Bunuel wrote:
roygush wrote:
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT

A. 125
B. 101
C. 77
D. 51
E. 41

I got this right but it took me 2 minutes.
I wonder if there is a quick way to solve this question without plugging numbers to X and Y.
I wrote down like 6 numbers with remainder of 7 and 3 and found each of the numbers from the answer choices manually.

I also tried the other approach X=12Q+7, Y=12R+3 and calculated 2X+Y but couldn't understand what to do next.
thanks

The remainder when x is divided by 12 is 7: $$x=12q+7$$ --> $$2x=24q+14$$.
The remainder when y is divided by 12 is 3: $$y=12p+3$$.

$$2x+y=(24q+14)+(12p+3)=24q+12p+12+5=12(2q+p+1)+5=(multiple \ of \ 12)+5$$. Only D is not a multiple of 12 plus 5.

bunuel, can we apply this method on any remainders problem?
write the two equations and then work from there?

I wouldn't say any, but $$dividend=divisor*quotient+remainder$$ formula is indeed very handy to deal with questions about remainders.

For more check GMAT Math Book chapter on remainders: remainders-144665.html

Hope it helps.
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Re: The integers x and y are both positive, the remainder when x [#permalink]  09 Sep 2014, 01:31
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Re: The integers x and y are both positive, the remainder when x   [#permalink] 09 Sep 2014, 01:31
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