• Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Remainder

This topic has 3 expert replies and 1 member reply
outty Junior | Next Rank: 30 Posts
Joined
14 Jan 2013
Posted:
14 messages

Remainder

Post Mon May 19, 2014 2:40 pm
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 63
e 53

d

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
Amrabdelnaby Master | Next Rank: 500 Posts Default Avatar
Joined
13 Nov 2015
Posted:
137 messages
Followed by:
2 members
Upvotes:
1
Top Reply
Post Thu Dec 24, 2015 12:33 pm
Hi Brent,

I think that there is a little mistake in your calculations here:

The remainder when y is divided by 12 is 3
Possible values of y = 3, 15, 28, 40, 52, ...

possible values of y should be 3, 15, 27,39,51,63. etc.....

You added 13 instead of 12 to 15 making you reach 28 instead of 27 and hence whatever followed was based on that, hence the following numbers need to be revised.

Cheers



Brent@GMATPrepNow wrote:
outty 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 63
e 53
Another approach is to test values.

IMPORTANT: When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, onto the question....

The remainder when x is divided by 12 is 7
Possible values of x = 7, 19, 31, 43, 55, ...
So, possible values of 2x = 14, 38, 62, 86, 110, ...

The remainder when y is divided by 12 is 3
Possible values of y = 3, 15, 28, 40, 52, ...

Each of the following is a possible value of 2x + y EXCEPT

A) 125 This equals 110 + 15. ELIMINATE A
B) 101 This equals 86 + 15. ELIMINATE B
C) 77 This equals 62 + 15. ELIMINATE C
D) 63
E) 53 This equals 38 + 15. ELIMINATE E

Answer: D

Cheers,
Brent

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post Mon May 19, 2014 5:31 pm
Hi outty,

I'm a big fan of TESTing VALUES on this question. Brent's approach showcases this tactic nicely. There is one aspect I would add to it: since this is an EXCEPT question, once you find the exception, you can stop working.

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

53 = 38 + 15. It's possible, so it's NOT what we're looking for.

63 though…using the possible values of 2X…

2X = 14; Y would have to be 49.
2X = 38; Y would have to be 25.
2X = 62; Y would have to be 1.

Y cannot be any of these options, so 63 is the option that is NOT possible…

Final Answer: D

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: outty
Amrabdelnaby Master | Next Rank: 500 Posts Default Avatar
Joined
13 Nov 2015
Posted:
137 messages
Followed by:
2 members
Upvotes:
1
Post Thu Dec 24, 2015 12:33 pm
Hi Brent,

I think that there is a little mistake in your calculations here:

The remainder when y is divided by 12 is 3
Possible values of y = 3, 15, 28, 40, 52, ...

possible values of y should be 3, 15, 27,39,51,63. etc.....

You added 13 instead of 12 to 15 making you reach 28 instead of 27 and hence whatever followed was based on that, hence the following numbers need to be revised.

Cheers



Brent@GMATPrepNow wrote:
outty 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 63
e 53
Another approach is to test values.

IMPORTANT: When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, onto the question....

The remainder when x is divided by 12 is 7
Possible values of x = 7, 19, 31, 43, 55, ...
So, possible values of 2x = 14, 38, 62, 86, 110, ...

The remainder when y is divided by 12 is 3
Possible values of y = 3, 15, 28, 40, 52, ...

Each of the following is a possible value of 2x + y EXCEPT

A) 125 This equals 110 + 15. ELIMINATE A
B) 101 This equals 86 + 15. ELIMINATE B
C) 77 This equals 62 + 15. ELIMINATE C
D) 63
E) 53 This equals 38 + 15. ELIMINATE E

Answer: D

Cheers,
Brent

  • +1 Upvote Post
  • Quote
  • Flag
Post Mon May 19, 2014 5:31 pm
Hi outty,

I'm a big fan of TESTing VALUES on this question. Brent's approach showcases this tactic nicely. There is one aspect I would add to it: since this is an EXCEPT question, once you find the exception, you can stop working.

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

53 = 38 + 15. It's possible, so it's NOT what we're looking for.

63 though…using the possible values of 2X…

2X = 14; Y would have to be 49.
2X = 38; Y would have to be 25.
2X = 62; Y would have to be 1.

Y cannot be any of these options, so 63 is the option that is NOT possible…

Final Answer: D

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: outty

Best Conversation Starters

1 lheiannie07 120 topics
2 LUANDATO 62 topics
3 swerve 62 topics
4 ardz24 61 topics
5 AAPL 57 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

174 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

173 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

131 posts
4 image description Jeff@TargetTestPrep

Target Test Prep

130 posts
5 image description EconomistGMATTutor

The Economist GMAT Tutor

130 posts
See More Top Beat The GMAT Experts