GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Jul 2018, 19:43

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

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
1 KUDOS received
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 635
Location: India
Find a possible value of a+b given the equations [#permalink]

Show Tags

New post 03 Jan 2013, 04:36
1
11
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:48) correct 39% (03:18) wrong based on 119 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

_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/best-online-gre-preparation.php

Improve Intuition and Your Score
Systematic Approaches

Expert Post
2 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8119
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
2
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
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 498
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member 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.

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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.