Remainder

Expert replies

outty: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Jan 14, 2013 1:41 pm

by outty » 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

Like this post

Source: Beat The GMAT — Problem Solving | Mon May 19, 2014 2:40 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon May 19, 2014 2:57 pm

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

d

When x is divided by 12, the remainder is 7.
Thus, x is a MULTIPLE OF 12 plus 7:
x = 12a + 7.

When y is divided by 12, the remainder is 3.
Thus, y is a MULTIPLE OF 12 plus 3:
y = 12b + 3.

Thus:
2x + y =

= 2(12a + 7) + 12b + 3

= 24a + 14 + 12b + 3

= 24a + 12b + 12 + 5

= 12(2a + b + 1) + 5.

Implication:
2x + y is a MULTIPLE OF 12 plus 5.

A: 125 = 12*10 + 5.
B: 101 = 12*8 + 5.
C: 77 = 12*6 + 5.
D: 63 = 12*5 + 3.
E: 53 = 12*4 + 5.

Only D is not a multiple of 12 plus 5.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon May 19, 2014 3:51 pm

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

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » 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 [email protected]

Like this post

Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » 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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review