When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?
A) 1
B) 3
C) 5
D) 7
E) 9
Answer: E
Source: www.gmatprepnow.com
Difficulty level: 600-650
When positive integer x is divided by 44
This topic has expert replies
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
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
Perfect!Shameilia wrote:x can equal 28 and y can equal 14. 28 + 14 = 42. 42 divided by 11 gives a remainder of 9.
Answer is E.
Many students overlook the fact that we can simply find an x-value and a y-value that satisfy the given information, and then use those values to determine the remainder when x+y is divided by 11.
So, x COULD equal 28, and y COULD equal 14, which means N = 28 + 14 = 42
When we divide 42 by 11, the remainder is 9.
There's also an algebraic solution.
Anyone?
Cheers,
Brent
-
- Master | Next Rank: 500 Posts
- Posts: 415
- Joined: Thu Oct 15, 2009 11:52 am
- Thanked: 27 times
Oh, all right.Brent@GMATPrepNow wrote:
There's also an algebraic solution.
Anyone?
X= 44N + 28 > first prompt
Y= 22M + 14 > second prompt
N=X+Y > N/11 = (X+Y)/11 = (44N + 22M + 42)/11
44N and 22M yield no remainders when divided by 11, only 42
42 = 3 + [spoiler]9/11[/spoiler] Remainder is 9
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
Beautiful!!regor60 wrote:Oh, all right.Brent@GMATPrepNow wrote:
There's also an algebraic solution.
Anyone?
X= 44N + 28 > first prompt
Y= 22M + 14 > second prompt
N=X+Y > N/11 = (X+Y)/11 = (44N + 22M + 42)/11
44N and 22M yield no remainders when divided by 11, only 42
42 = 3 + [spoiler]9/11[/spoiler] Remainder is 9
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
Regor60's algebraic solution (above) is perfect.Brent@GMATPrepNow wrote:When positive integer x is divided by 44, the remainder is 28. When positive integer y is divided by 22, the remainder is 14. If N = x+y, what is the remainder when N is divided by 11?
A) 1
B) 3
C) 5
D) 7
E) 9
In case some viewers are unfamiliar with this technique, here's a longer version:
When it comes to remainder questions, there's a useful rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
When x is divided by 44, the remainder is 28
We can rewrite this as "x divided by 44 equals some integer k with remainder 28"
So, x = 44k + 28 for some integer k
When integer y is divided by 22, the remainder is 14.
So, y = 22j + 14 for some integer j
N = x + y = (44k + 28) + (22j + 14)
N = 44k + 22j + 42
N = 44k + 22j + 33 + 9
N = 11(4k + 2j + 3) + 9
As we can see N is 9 GREATER than some multiple of 11
So, when we divide N by 11, the remainder will be 9
Answer: E