It is currently 22 Feb 2018, 18:37

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M26-27

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
M26-27 [#permalink]

Show Tags

New post 16 Sep 2014, 00:26
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (01:19) correct 37% (01:45) wrong based on 51 sessions

HideShow timer Statistics

\(x\), \(y\) 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
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re M26-27 [#permalink]

Show Tags

New post 16 Sep 2014, 00:26
Expert's post
3
This post was
BOOKMARKED
Official Solution:

\(x\), \(y\) 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


Given \(x=qy+3\), where \(q\) is a quotient, an integer \(\ge 0\). Which means that the least value of \(x\) is when \(q=0\), in that case \(x=3\). This basically means that \(x\) is less than \(y\). For example 3 divided by 4 yields the remainder of 3.

According to the above:

\(x\) is divided by \(y\) the remainder is 3 means that the minimum value of \(x\) is 3;

\(y\) is divided by \(z\) the remainder is 8 means that the minimum value of \(y\) is 8 and the minimum value of \(z\) is one more than 8, so 9 (8 divided by 9 yields the remainder of 8);

So, the smallest possible value of \(x+y+z\) is \(3+8+9=20\).


Answer: B
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 02 Sep 2014
Posts: 89
Location: United States
Schools: Haas EWMBA '20
GMAT 1: 770 Q50 V44
GPA: 3.97
GMAT ToolKit User Reviews Badge
Re: M26-27 [#permalink]

Show Tags

New post 08 Jun 2015, 20:58
wow I guessed this one but its a brilliant problem! Beautiful!
Intern
Intern
avatar
Joined: 14 Jun 2014
Posts: 7
GMAT ToolKit User
Re M26-27 [#permalink]

Show Tags

New post 05 Dec 2015, 01:18
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4
Intern
Intern
avatar
Joined: 23 Mar 2016
Posts: 14
Re: M26-27 [#permalink]

Show Tags

New post 16 Sep 2016, 00:29
please explain..
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4
:( :( :roll:
please can anyone explain me this problem in easy way :cry:
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: M26-27 [#permalink]

Show Tags

New post 16 Sep 2016, 01:04
1 KUDOS received
Manager
Manager
User avatar
B
Joined: 30 Oct 2012
Posts: 67
Location: India
WE: Marketing (Manufacturing)
M26-27 [#permalink]

Show Tags

New post 16 Sep 2016, 01:21
1
This post received
KUDOS
Karanagrawal wrote:
please explain..
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4
:( :( :roll:
please can anyone explain me this problem in easy way :cry:


See x has to be at least 3 for a remainder of 3 when x is divided by y.

then x = 3.

y has to be greater than 3 for x/y to get a remainder of 3,

and y has to be at least 8 for y/z to get a remainder of 8.

then y = 8.

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

So going with z = 9.

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

It’s not over until I say it’s over

1 KUDOS received
Manager
Manager
User avatar
B
Joined: 30 Oct 2012
Posts: 67
Location: India
WE: Marketing (Manufacturing)
Re: M26-27 [#permalink]

Show Tags

New post 16 Sep 2016, 01:43
1
This post received
KUDOS
Karanagrawal wrote:
please explain..
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4
:( :( :roll:
please can anyone explain me this problem in easy way :cry:


Remember this rule:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
_________________

It’s not over until I say it’s over

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5660
M26-27 [#permalink]

Show Tags

New post 16 Sep 2016, 02:06
1
This post received
KUDOS
Expert's post
Karanagrawal wrote:
please explain..
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4
:( :( :roll:
please can anyone explain me this problem in easy way :cry:


Hi,
X as 2 and y as 4 is clearly incorrect...

Now for this Q, my advice would be talk of larger number first...

1) If y is divided by z, remainder is 8..
This tells us that least value of y is 8 and the remainder will be 8, ONLY if z is greater than 8, so take the next least possible value..
And it is 8+1=9...

2) now take the second part..
If x is divided by y, remainder is 3..
Since least value of y is 8, x will be 3 or 11 or 19 and so on to leave remainder of 3..
But we have to take least value and it is 3..

So x can be 3, y can be 8 and z can be 9..
Ans x+y+z=3+8+9=20
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Manager
Manager
avatar
B
Joined: 10 Feb 2017
Posts: 60
Location: India
GMAT 1: 680 Q50 V30
GPA: 3.9
Reviews Badge
Re: M26-27 [#permalink]

Show Tags

New post 23 Mar 2017, 10:18
deospaima wrote:
if x divided by y the reminder is 3 then y > 3 , not x . example : x=2 ; y=4


as stated minimum value of x=3 and y>3 it means for minimum value of X y>x

see eg: x=3 and y=4 this means when x is divided by y remainder is 3 and y>remainder i.e. 3 but in this case y if >3 will also be greater than x ultimately.
Intern
Intern
avatar
B
Joined: 12 Dec 2016
Posts: 2
CAT Tests
Re M26-27 [#permalink]

Show Tags

New post 12 Aug 2017, 07:12
I think this is a high-quality question and I agree with explanation.
Intern
Intern
avatar
B
Joined: 07 Aug 2016
Posts: 17
Location: Brazil
Concentration: Economics, Marketing
WE: Project Management (Energy and Utilities)
GMAT ToolKit User CAT Tests
Re: M26-27 [#permalink]

Show Tags

New post 18 Oct 2017, 15:31
Would this method be wrong?

x/y -> remainder = 3
therefore y = x+3

y/z -> remainder of 8
therefore z = x+ 8

x+ 8 + x + x+ 3 = 11 + 3x - the least multiple of 3 that results in any answer is 3

therefore 3*3 + 11 = 20
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: M26-27 [#permalink]

Show Tags

New post 18 Oct 2017, 20:13
zzarur wrote:
Would this method be wrong?

x/y -> remainder = 3
therefore y = x+3

y/z -> remainder of 8
therefore z = x+ 8

x+ 8 + x + x+ 3 = 11 + 3x - the least multiple of 3 that results in any answer is 3

therefore 3*3 + 11 = 20


How does x divided by y gives the remainder of 3 translates to y = x + 3?
How does y divided by z gives the remainder of 8 translates to z = x + 8?

Check solution here: https://gmatclub.com/forum/m26-184466.html#p1415594
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 02 Sep 2017
Posts: 10
Reviews Badge
Re: M26-27 [#permalink]

Show Tags

New post 24 Dec 2017, 03:48
Given:
x=y(integer) + 3

y=z(integer) + 8

Therefore, x=z(integer) +8 + 3

x + y + z = [z(integer) +8 + 3] + [z(integer) + 8] + z = z(0) + 8 + 3+ z(0) + 8 + z = 19 + z

Minimum possible value of z = 1

thus, x + y + z = 19 + 1 = 20
Re: M26-27   [#permalink] 24 Dec 2017, 03:48
Display posts from previous: Sort by

M26-27

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.