It is currently 19 Nov 2017, 09:21

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

Find a possible value of a+b given the equations

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

Hide Tags

Expert Post
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 534 [0], given: 16

Location: India
Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 03 Jan 2013, 04:36
Expert's post
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

60% (02:50) correct 40% (03:18) wrong based on 113 sessions

HideShow timer Statistics

If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20
[Reveal] Spoiler: OA

_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Premium Material
Standardized Approaches

Kudos [?]: 534 [0], given: 16

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17797 [2], given: 235

Location: Pune, India
Re: Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 03 Jan 2013, 10:30
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
SravnaTestPrep wrote:
If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20


Too many variables! I will try to look at the big picture here.
We have two equations:
\(ax + by = 17\) ,
\(2ax + 3by = 43\)

Twice of (ax + by) will be 34 so we get that 'by' must be 43 - 34 = 9
If by = 9, ax must be 17 - 9 = 8

Now, x/y = 2/3
ax/by = (a/b)*(2/3) = 8/9
So a/b = 4/3

Since a and b are integers, many such solutions are possible: a = 4, b = 3 OR a = 8, b = 6 etc. a+b will be 7/14/21...
Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17797 [2], given: 235

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15658

Kudos [?]: 282 [0], given: 0

Premium Member
Re: Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 14 Sep 2015, 09:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 282 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15658

Kudos [?]: 282 [0], given: 0

Premium Member
Re: Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 15 Nov 2016, 12:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 282 [0], given: 0

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2017
Posts: 371

Kudos [?]: 70 [0], given: 66

GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 11 Sep 2017, 03:59
SravnaTestPrep wrote:
If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20



ax+by=17
2ax+3by=43

multiply first equation by 2 and subtract from 2nd => by=9
multiply 1st equation by 3 and subtract 2nd from it => ax=8

ax=8 and by=9

3x=2y

ax=8
a3x=24
a2y=24
ay=12

ay=12 by=9
a:b= 12/9
starting from least a:b can be => 4:3, 8:6 , 12:9
but second is is that in which we are interested in

a:b = 8:6
a=8 b = 6 a+b =14 OPTION C IS THE ANSWER
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 70 [0], given: 66

Re: Find a possible value of a+b given the equations   [#permalink] 11 Sep 2017, 03:59
Display posts from previous: Sort by

Find a possible value of a+b given the equations

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


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®.