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

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Manager
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The integers x and y are both positive, the remainder when x [#permalink] New post 05 Jan 2013, 13:17
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69% (04:03) correct 31% (01:48) wrong based on 52 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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Last edited by Bunuel on 07 Jan 2013, 03:29, edited 2 times in total.
Edited the question.
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Kudos [?]: 349 [0], given: 182

Re: The integers x and y are both positive, the remainder when x [#permalink] New post 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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Kudos [?]: 19 [0], given: 19

Re: The integers x and y are both positive, the remainder when x [#permalink] New post 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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IMPOSSIBLE IS NOTHING

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Re: The integers x and y are both positive, the remainder when x [#permalink] New post 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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Re: The integers x and y are both positive, the remainder when x [#permalink] New post 07 Jan 2013, 03:34
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.

Answer: D.
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Manager
Manager
User avatar
Joined: 01 Sep 2012
Posts: 124
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Kudos [?]: 19 [0], given: 19

Re: The integers x and y are both positive, the remainder when x [#permalink] New post 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.

Answer: D.


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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25253
Followers: 3430

Kudos [?]: 25267 [0], given: 2702

Re: The integers x and y are both positive, the remainder when x [#permalink] New post 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.

Answer: D.


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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The integers x and y are both positive, the remainder when x   [#permalink] 07 Jan 2013, 08:44
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