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The integers x and y are both positive, the remainder when x [#permalink]
 05 Jan 2013, 14:17
Question Stats:
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37% (01:40) wrong based on 1 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
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Last edited by Bunuel on 07 Jan 2013, 04:29, edited 2 times in total.
Edited the question.
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Re: The integers x and y are both positive, the remainder when x [#permalink]
05 Jan 2013, 15:24
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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Re: The integers x and y are both positive, the remainder when x [#permalink]
06 Jan 2013, 00:59
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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Re: The integers x and y are both positive, the remainder when x [#permalink]
06 Jan 2013, 01:50
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]
07 Jan 2013, 04:34
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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Re: The integers x and y are both positive, the remainder when x [#permalink]
07 Jan 2013, 07:04
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?
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Re: The integers x and y are both positive, the remainder when x [#permalink]
07 Jan 2013, 09:44
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.htmlHope it helps.
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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. NEW!!!
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. NEW!!!
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Re: The integers x and y are both positive, the remainder when x
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07 Jan 2013, 09:44
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