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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Remainder
This topic has expert replies
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
When x is divided by 12, the remainder is 7.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
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
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
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Another approach is to test values.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
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
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
-
Amrabdelnaby
- Master | Next Rank: 500 Posts
- Posts: 137
- Joined: Fri Nov 13, 2015 11:01 am
- Thanked: 1 times
- Followed by:2 members
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
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:Another approach is to test values.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
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
