Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 May 2016, 06:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 01 Sep 2012
Posts: 128
Followers: 1

Kudos [?]: 81 [1] , given: 19

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

### Show Tags

05 Jan 2013, 14:17
1
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (03:14) correct 33% (02:05) wrong based on 205 sessions

### HideShow timer Statistics

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

_________________

If my answer helped, dont forget KUDOS!

IMPOSSIBLE IS NOTHING

Last edited by Bunuel on 07 Jan 2013, 04:29, edited 2 times in total.
Edited the question.
Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 68

Kudos [?]: 634 [0], given: 183

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

### Show Tags

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?
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Current Student
Joined: 01 Sep 2012
Posts: 128
Followers: 1

Kudos [?]: 81 [0], given: 19

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

### Show Tags

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.
_________________

If my answer helped, dont forget KUDOS!

IMPOSSIBLE IS NOTHING

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 164

Kudos [?]: 1066 [0], given: 62

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

### Show Tags

06 Jan 2013, 01:50
Expert's post
1
This post was
BOOKMARKED
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32963
Followers: 5743

Kudos [?]: 70354 [5] , given: 9844

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

### Show Tags

07 Jan 2013, 04:34
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Current Student
Joined: 01 Sep 2012
Posts: 128
Followers: 1

Kudos [?]: 81 [0], given: 19

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

### Show Tags

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.

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: 32963
Followers: 5743

Kudos [?]: 70354 [0], given: 9844

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

### Show Tags

07 Jan 2013, 09:44
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9607
Followers: 465

Kudos [?]: 120 [0], given: 0

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

### Show Tags

09 Sep 2014, 02:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 06 Jul 2011
Posts: 132
Followers: 0

Kudos [?]: 48 [0], given: 240

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

### Show Tags

25 Jun 2015, 06:30
x= 12q+7 => 2x = 24q+14
y = 12p+3

2x+y = 24q+14+12p+3 => 12(p+2q)+17

Any answer choice from which 17 is subtracted and it doesn't turn out to be a multiple of 12 is the answer. => 51-17 = 34 (not a multiple of 12).

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 443
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Followers: 1

Kudos [?]: 83 [0], given: 169

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

### Show Tags

30 Jul 2015, 09:04
Another way to do it is the following, which took me around 4 minutes (perhaps someone quick in calculations could do it faster, dunno...). So:

x=12q+7 = 19, 31, 43, 55, 67 etc. Doudling it: 38, 62, 126, 110, 134 etc.
y=12z+3 = 15, 27, 39, 51, 63 etc.

At this point, we can already see that D is the answer, as D=51, which is a possible value of y alone. So, it is not possible that if we add x to 51 it will remain 51. So, ANS D

Do you think it is doable like this in under 2 minutes, even though it took me 4? I am asking as I am terribly slow in calculations. Performing calculations is a serious problem of mine in gmat...
Intern
Joined: 08 Nov 2014
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 12

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

### Show Tags

30 Jul 2015, 09:17
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

Hi,

x/12 = 7 (remainder) and y/12 = 3 (remainder). Hence the least value of x has to be 7 and least value of y is 3. Therefore, 2x+y = 17. Hence, look for an answer choice that is a multiple of 17, which is 51.

Ans - D
Intern
Joined: 08 Nov 2014
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 12

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

### Show Tags

30 Jul 2015, 09:20
pacifist85 wrote:
Another way to do it is the following, which took me around 4 minutes (perhaps someone quick in calculations could do it faster, dunno...). So:

x=12q+7 = 19, 31, 43, 55, 67 etc. Doudling it: 38, 62, 126, 110, 134 etc.
y=12z+3 = 15, 27, 39, 51, 63 etc.

At this point, we can already see that D is the answer, as D=51, which is a possible value of y alone. So, it is not possible that if we add x to 51 it will remain 51. So, ANS D

Do you think it is doable like this in under 2 minutes, even though it took me 4? I am asking as I am terribly slow in calculations. Performing calculations is a serious problem of mine in gmat...

Hi,

x/12 = 7 (remainder) and y/12 = 3 (remainder). Hence the least value of x has to be 7 and least value of y is 3. Therefore, 2x+y = 17. Hence, look for an answer choice that is a multiple of 17, which is 51.

Ans - D

The above method, if used, can be solved within 2 mins. I took 1.5 mins to do so.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 6380
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 267

Kudos [?]: 1884 [1] , given: 160

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

### Show Tags

30 Jul 2015, 15:27
1
KUDOS
Expert's post
Hi All,

I'm a big fan of TESTing VALUES on this question along with a bit of 'brute force' math (pacifist85's approach showcases this tactic nicely). There is one detail worth noting and one aspect I would add to it: since this is an EXCEPT question, once you find the exception, you can stop working.

The detail in pacifist85s math is that Q and Z could both be 0, so X COULD = 7 (and by extension, 2X COULD = 14) and Y COULD = 3.

I would start with answer E because it's smallest (so it would have the least number of possible sums that could equal it).

41 = 38 + 3. It's possible, so it's NOT what we're looking for.

51 though…using the possible values of 2X…

2X = 14; Y would have to be 37 (which is NOT possible).
2X = 38; Y would have to be 13 (which is NOT possible).
2X = 62; this is already TOO BIG.

Thus, 51 is the option that is NOT possible…

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: The integers x and y are both positive, the remainder when x   [#permalink] 30 Jul 2015, 15:27
Similar topics Replies Last post
Similar
Topics:
13 If x and y are both positive integers, what is the remainder when 2*10 8 26 May 2015, 07:10
If x and y are both positive integers and x>y, what the remainder when 2 02 May 2015, 02:07
39 If x and y are positive integers, what is the remainder when 22 04 Aug 2010, 15:17
8 If x and y are positive integer, what is the remainder when 5 02 Nov 2009, 07:15
7 If x and y are positive integers, what is the remainder when 6 01 Jul 2008, 15:57
Display posts from previous: Sort by