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 →

Remainder Sum from Manhattan NP Book

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Wed Sep 25, 2013 9:38 am
by Premalatha Anand » Fri Oct 04, 2013 10:59 am
If X and Y are positive integers and x/y has a remainder of 5, what is the smallest possible value of XY?


Ans is 30
Remainder cannot be larger than Y, so Y should be at least 6.

But my que is how can the smallest possible value of X can be 5??

Please explain!
Regards
Premalatha
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members
Thanked: 1443 times

by ceilidh.erickson » Fri Oct 04, 2013 11:05 am
If 5 is divided by 6, the result is 0 remainder 5. The remainder must be smaller than Y, but there's no rule that says that X has to be larger than Y.

If you divide X by a larger integer Y, the result will be 0 remainder X.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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 » Fri Oct 04, 2013 11:08 am
Premalatha Anand wrote:If X and Y are positive integers and x/y has a remainder of 5, what is the smallest possible value of XY?


Ans is 30
Remainder cannot be larger than Y, so Y should be at least 6.

But my que is how can the smallest possible value of X can be 5??

Please explain!
There a two important rules regarding remainders

#1) If N divided by D, leaves remainder R, then 0 < R < D

#2) 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.

IMPORTANT: Notice that 1 is the smallest possible value of k. A lot of people miss this. However, 1 divided by 5 equals 0 with remainder 1. In other words, 5 divides into 1 zero times with remainder 1.

For this question, we're told that x divided by y has a remainder of 5. So, the possible values of x are: 5, 5 + y, 5 + 2y, 5 + 3y, 5 + 4y, etc.

So, the SMALLEST value of x is 5.
For the division (x divided by y) leaves a remainder of 5, y must be greater than 5.
So, the SMALLEST value of y is 6

So, the SMALLEST value of xy = (5)(6) = 30

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Wed Sep 25, 2013 9:38 am

by Premalatha Anand » Fri Oct 04, 2013 12:07 pm
Thanks Erickson. Didn't know the rule.

Thanks brent for the detailed explanation!.
Regards
Premalatha
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Fri Oct 04, 2013 7:12 pm
Brent@GMATPrepNow wrote:
Premalatha Anand wrote:If X and Y are positive integers and x/y has a remainder of 5, what is the smallest possible value of XY?


Ans is 30
Remainder cannot be larger than Y, so Y should be at least 6.

But my que is how can the smallest possible value of X can be 5??

Please explain!
There a two important rules regarding remainders

#1) If N divided by D, leaves remainder R, then 0 < R < D

#2) 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.

IMPORTANT: Notice that 1 is the smallest possible value of k. A lot of people miss this. However, 1 divided by 5 equals 0 with remainder 1. In other words, 5 divides into 1 zero times with remainder 1.

For this question, we're told that x divided by y has a remainder of 5. So, the possible values of x are: 5, 5 + y, 5 + 2y, 5 + 3y, 5 + 4y, etc.

So, the SMALLEST value of x is 5.
For the division (x divided by y) leaves a remainder of 5, y must be greater than 5.
So, the SMALLEST value of y is 6

So, the SMALLEST value of xy = (5)(6) = 30

Cheers,
Brent
Brent, does this mean that "R" is always less than D"
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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 » Fri Oct 04, 2013 7:14 pm
vinay1983 wrote: Brent, does this mean that "R" is always less than D"
Yes.

Cheers,
Brent
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
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] » Sat Oct 05, 2013 1:22 pm
Hi Premalatha Anand,

I think that all of the other posts in this string have provided the proper insight to answer your initial question, so I'm just going to take a moment to reiterate an important point.

Since "remainder" questions/concepts will usually show up 1-2 times on Test Day, it's worth remembering that remainders are "left over" pieces and the smallest possible numerator in these situations is the one that leads to 0 r <number>.

For example: 3/5 = 0 r 3

Keep this rule in mind any time a "remainder" question appears. It will usually make the question easier to solve.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Wed Sep 25, 2013 9:38 am

by Premalatha Anand » Sun Oct 06, 2013 8:16 am
Rich,

Easy to remember! Wont forget hereafter. Thanks!
Regards
Premalatha
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1