NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 15:49 It is currently 24 Apr 2024, 15:49
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The integers a, b, and c are positive a/b = 5/2, and a/c

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
Chembeti
Manager
Manager
Joined: 25 Nov 2011
Posts: 126
Own Kudos [?]: 870 [20]
Given Kudos: 20
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE:Information Technology (Computer Software)
Send PM
The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   26 Feb 2012, 00:21
3
Kudos
17
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:55) correct 18% (02:15) wrong based on 356 sessions
Hide Show timer Statistics
The integers a, b, and c are positive, a/b = 5/2, and a/c = 7/5. What is the smallest possible value of 2a + b?

A. 63
B. 70
C. 84
D. 95
E. 105
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618809 [6]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   26 Feb 2012, 00:30
2
Kudos
4
Bookmarks
Expert Reply
Chembeti wrote:
The integers a, b, and c are positive, a/b = 5/2, and a/c = 7/5. What is the smallest possible value of 2a + b?

A. 63
B. 70
C. 84
D. 95
E. 105


Since \(\frac {a}{b}=\frac {5}{2}\), and \(\frac {a}{c}=\frac {7}{5}\) then \(a\) must be a multiple of both 5 and 7, so the lowest value of \(a\) is \(5*7=35\) (note that \(a\) is a positive integer). Then the lowest value of \(b\) would be \(2*7=14\), as \(\frac {a}{b}=\frac {5}{2}=\frac {5*7}{2*7}=\frac {35}{14}\), so the lowest value of \(2a+b=2*35+14=84\).

Answer: C.

Or: since \(\frac {a}{b}=\frac {5}{2}\) then \(a=\frac{5b}{2}\) and \(2a + b=2*\frac{5b}{2}+b=6b\), so it's a multiple of 6. The only multiple of 6 among the answer choices is 84 (C).

Answer: C.
General Discussion
User avatar
pharm
Intern
Intern
Joined: 03 Jan 2013
Posts: 15
Own Kudos [?]: [0]
Given Kudos: 50
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   04 Feb 2013, 08:15
why is the value of '2' for b have '7' multiplying to it , 7 is the the value for the fraction a/c . I understand how you are getting the lowest value for 'a' but not for 'b' .

Thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618809 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   04 Feb 2013, 08:23
Expert Reply
pharm wrote:
why is the value of '2' for b have '7' multiplying to it , 7 is the the value for the fraction a/c . I understand how you are getting the lowest value for 'a' but not for 'b' .

Thanks


The lowest value of a is 35. Now, if a=35, then from a/b = 5/2 we'll have that b=14.

Hope it's clear.
User avatar
pharm
Intern
Intern
Joined: 03 Jan 2013
Posts: 15
Own Kudos [?]: [0]
Given Kudos: 50
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   04 Feb 2013, 08:39
Ok so since a/b = 5/2 and a/c = 7/5 . You are multiple across the '7' to 5 & 2 in order to get their LCM. Correct?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618809 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   04 Feb 2013, 08:42
Expert Reply
pharm wrote:
Ok so since a/b = 5/2 and a/c = 7/5 . You are multiple across the '7' to 5 & 2 in order to get their LCM. Correct?


I don't understand what you mean. Please, elaborate your question.
User avatar
pharm
Intern
Intern
Joined: 03 Jan 2013
Posts: 15
Own Kudos [?]: [0]
Given Kudos: 50
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   04 Feb 2013, 08:58
Bunuel wrote:
pharm wrote:
why is the value of '2' for b have '7' multiplying to it , 7 is the the value for the fraction a/c . I understand how you are getting the lowest value for 'a' but not for 'b' .

Thanks


The lowest value of a is 35. Now, if a=35, then from a/b = 5/2 we'll have that b=14.

Hope it's clear.



you said that from a/b = 5/2 , b=14 . Since in a/b , 'b' was = 2 . the common number is '7' that is being multipled to 5 and 2 in order to reach the lowest possible values correct?
so to get " b's " lowest possible value you multiplied = '2 * 7= 14' . Does '7' hold any significance that it was used for the values in 'a' & 'b' to reach there lowest possible values ?
User avatar
Kris01
Manager
Manager
Joined: 24 Sep 2012
Posts: 68
Own Kudos [?]: 410 [0]
Given Kudos: 3
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE:Education (Education)
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   16 Feb 2013, 15:57
It is mentioned that a/c=7/5. So from this ratio we know that 7 needs to be a factor of a. From a/b=5/2 we again know that a must contain 5. Hence, the minimum value of a must be 35.

Using the ratio a/b=5/2, we know that b must have 2 and must also contain 7 as a also contained 7 which was cancelled while calculating he simplest form of ratio.

pharm wrote:
Bunuel wrote:
pharm wrote:
why is the value of '2' for b have '7' multiplying to it , 7 is the the value for the fraction a/c . I understand how you are getting the lowest value for 'a' but not for 'b' .

Thanks


The lowest value of a is 35. Now, if a=35, then from a/b = 5/2 we'll have that b=14.

Hope it's clear.



you said that from a/b = 5/2 , b=14 . Since in a/b , 'b' was = 2 . the common number is '7' that is being multipled to 5 and 2 in order to reach the lowest possible values correct?
so to get " b's " lowest possible value you multiplied = '2 * 7= 14' . Does '7' hold any significance that it was used for the values in 'a' & 'b' to reach there lowest possible values ?
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   22 Apr 2014, 03:38
\(\frac{a}{b} = \frac{5}{2}\)

\(\frac{2a}{b} = \frac{10}{2}\)

Using componendo / dividendo

\(\frac{2a + b}{b} = \frac{10+2}{2}\)

2a +b = 6b

Looking at the options available, only 84 is divisible by 6

Answer = C

Bunuel, can you kindly tell-

Q1: Is this method correct to solve?

Q2: a/c = 7/5 >> Is this term given just to confuse? As I never required that info in solving this problem.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18756
Own Kudos [?]: 22047 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   02 May 2017, 16:48
1
Bookmarks
Expert Reply
Chembeti wrote:
The integers a, b, and c are positive, a/b = 5/2, and a/c = 7/5. What is the smallest possible value of 2a + b?

A. 63
B. 70
C. 84
D. 95
E. 105


We are given that:

a/b = 5/2 or a : b = 5 : 2

and

a/c = 7/5 or a : c = 7 : 5

We need to determine the smallest value of 2a + b.

Since a is a multiple of 5 and of 7, we see it’s a multiple of the LCM of 5 and 7, which is 35.

Thus we now have:

a : b = 5 x 7 : 2 x 7 = 35 : 14

a : c = 7 x 5 : 5 x 5 = 35 : 25

So the minimum value of a is 35 and the minimum value of b is 14 (since a, b, and c must be integers), and thus the minimum value of 2a + b is 2(35) + 14 = 70 = 14 = 84.

Answer: C
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [1]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   26 Jul 2018, 11:23
1
Kudos
Chembeti wrote:
The integers a, b, and c are positive, a/b = 5/2, and a/c = 7/5. What is the smallest possible value of 2a + b?

A. 63
B. 70
C. 84
D. 95
E. 105


\(\frac{a}{b} = \frac{5}{2}\), & \(\frac{a}{c} = \frac{7}{5}\)

Make numerators same base

So, \(\frac{a}{b} = \frac{35}{14}\), & \(\frac{a}{c} = \frac{35}{25}\)

So We have \(a = 35\), \(b = 14\) & \(c = 25\)

Thus, The value of \(2a + b = 2*35 + 14 = 84\), Answer must be (C)
User avatar
B
Mansoor50
Manager
Manager
Joined: 29 May 2017
Posts: 154
Own Kudos [?]: 19 [0]
Given Kudos: 63
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Send PM
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink] New post   21 Nov 2018, 19:57
JUst in case its not obvious that a is a multiple of 35:

b/a + c/a = 2/5 + 5/7

(b+c)/a = 39/35

this clearly shows that a is a multiple of 35
GMAT Club Bot
gmatclubot
Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
21 Nov 2018, 19:57
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions