BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

When positive integer x is divided by 44

Expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
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 » Thu Mar 30, 2017 7:34 am
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Thu Sep 23, 2010 11:42 am

by Shameilia » Thu Mar 30, 2017 7:40 am
x can equal 28 and y can equal 14. 28 + 14 = 42. 42 divided by 11 gives a remainder of 9.
Answer is E.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Thu Mar 30, 2017 7:52 am
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.
Perfect!
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

by regor60 » Thu Mar 30, 2017 8:30 am
Brent@GMATPrepNow wrote:
There's also an algebraic solution.
Anyone?
Oh, all right.

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Thu Mar 30, 2017 8:49 am
regor60 wrote:
Brent@GMATPrepNow wrote:
There's also an algebraic solution.
Anyone?
Oh, all right.

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
Beautiful!!
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Thu Mar 30, 2017 8:55 am
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
Regor60's algebraic solution (above) is perfect.
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1