• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## remainder and min max

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 1 member reply
buoyant Master | Next Rank: 500 Posts
Joined
02 Mar 2013
Posted:
106 messages
Thanked:
4 times

#### remainder and min max

Mon Jan 19, 2015 12:30 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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

OA:B

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
Marty Murray Legendary Member
Joined
03 Feb 2014
Posted:
2037 messages
Followed by:
129 members
Thanked:
948 times
GMAT Score:
800
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

OA:B
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
GMAT Coach
m.w.murray@hotmail.com
http://infinitemindprep.com/
In Person in the New York Area and Online Worldwide

Thanked by: buoyant

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13361 messages
Followed by:
1779 members
Thanked:
12885 times
GMAT Score:
790
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.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Thanked by: sarthak.agarwal, buoyant
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
10763 messages
Followed by:
1212 members
Thanked:
5146 times
GMAT Score:
770
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

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 – Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

Thanked by: buoyant
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2560 messages
Followed by:
113 members
Thanked:
581 times
Target GMAT Score:
V51
GMAT Score:
780
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.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### Best Conversation Starters

1 Vincen 180 topics
2 lheiannie07 65 topics
3 Roland2rule 49 topics
4 ardz24 44 topics
5 LUANDATO 23 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

147 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

103 posts
3 GMATGuruNY

The Princeton Review Teacher

102 posts
4 EconomistGMATTutor

The Economist GMAT Tutor

94 posts
5 DavidG@VeritasPrep

Veritas Prep

76 posts
See More Top Beat The GMAT Experts