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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

remainder and min max

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 106
Joined: Sat Mar 02, 2013 4:29 pm
Thanked: 4 times
by buoyant » Mon Jan 19, 2015 12:30 pm
x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33

[spoiler]OA:B[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2135
Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members
Location: https://martymurraycoaching.com/
Thanked: 955 times
GMAT Score:800

by MartyMurray » Mon Jan 19, 2015 1:19 pm
buoyant wrote:x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33

[spoiler]OA:B[/spoiler]
Well, x has to be a least 3 for a remainder of 3 when x is divided by y.

So going to say x = 3.

y has to be greater than 3 for x/y to generate a remainder of 3, and y has to be at least 8 for y/z to generate a remainder of 8.

So going to say y = 8.

Z has to be greater than 8 for y/z to generate a remainder of 8. Lowest possible integer greater than 8 is 9.

So going with z = 9.

x + y + z = 3 + 8 + 9 = 20

Choose B.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
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 Jan 19, 2015 1:24 pm
buoyant wrote:x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33
When y is divided by z, the remainder is 8.
In other words, y is 8 more than a multiple of z:
y = az + 8, where a is a nonnegative integer.

The smallest possible value of y occurs when a=0:
y = 0*z + 8 = 8.

If y=8, then the statement above becomes:
When y=8 is divided by z, the remainder is 8.

For 8/z to have a remainder of 8, z must be GREATER than 8.
To illustrate:
If z=1, then 8/z = 8/1 = 8 R0.
If z=2, then 8/z = 8/2 = 4 R0.
If z=3, then 8/z = 8/3 = 2 R2.
If z=4, then 8/z = 8/4 = 2 R0.
If z=5, then 8/z = 8/5 = 1 R3.
If z=6, then 8/z = 8/6 = 1 R2.
If z=7, then 8/z = 8/7 = 1 R1.
If z=8, then 8/z = 8/8 = 1 R0.
If z=9, then y/z = 8/9 = 0 R8.
Thus, the smallest possible value of z = 9.

When x is divided by y, the remainder is 3.
In other words, x is 3 more than a multiple of y:
x = by + 3, where b is a nonnegative integer.

The smallest possible value of x occurs when b=0
x = 0*y + 3 = 3.

Thus:
Smallest possible value of x+y+z = 3+8+9 = 20.

The correct answer is B.
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
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 » Mon Jan 19, 2015 1:44 pm
buoyant wrote:x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
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.

-------------------------

When y is divided by z the remainder is 8
According to the above rule, the possible values of y are: 8, 8+z, 8+2z, 8+3z...
We want to MINIMIZE the value of y, so y = 8

When x is divided by y the remainder is 3
Now that we know that y = 8, we can write: When x is divided by 8 the remainder is 3
According to the above rule, the possible values of x are: 3, 3 + 8, 3 + 2(8)...
We want to MINIMIZE the value of x, so x = 3

What about z????
We already know that, when y is divided by z, the remainder is 8
There's a rule that says, when positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
So, for the given information, we can conclude that 0 < 8 < z
We want to MINIMIZE the value of z, so z = 9

So, the smallest possible value of x+y+z =3 + 8 + 9
= 20
= B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Sun Jan 25, 2015 4:28 pm
Marty Murray wrote:Well, x has to be a least 3 for a remainder of 3 when x is divided by y.

So going to say x = 3.
Well ... this is mathematical Catch-22, where anyone who could follow it would already know what to do. For the perplexed, what Marty is doing here is exploiting the fact that if we're dividing integers in the remainder system, we have

x/y = 0, with remainder x

if y > x > 0. For instance, 3/5 = 0, with remainder 3; 4/7 = 0, with remainder 4, etc. So x is at least 3 greater than a multiple of y, and since we want the minimum value of x, we can make x = 3 and "a multiple of y" = 0, since 0 is a multiple of any integer.

This is worth delving into a bit, as most students will struggle with it.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1