Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 25 Nov 2011
Posts: 250
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)

The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
26 Feb 2012, 00:21
1
This post received KUDOS
6
This post was BOOKMARKED
Question Stats:
79% (02:38) correct
21% (01:48) wrong based on 231 sessions
HideShow 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
 Aravind Chembeti



Math Expert
Joined: 02 Sep 2009
Posts: 39751

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
26 Feb 2012, 00:30
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 03 Jan 2013
Posts: 15

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 39751

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
04 Feb 2013, 08:23



Intern
Joined: 03 Jan 2013
Posts: 15

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
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?



Math Expert
Joined: 02 Sep 2009
Posts: 39751

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
04 Feb 2013, 08:42



Intern
Joined: 03 Jan 2013
Posts: 15

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
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 ?



Manager
Joined: 24 Sep 2012
Posts: 90
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE: Education (Education)

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
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 ?



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
09 Apr 2014, 10:34
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



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
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.
_________________
Kindly press "+1 Kudos" to appreciate



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
16 Dec 2015, 02:06
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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
28 Apr 2017, 05:19
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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1158
Location: United States (CA)

Re: The integers a, b, and c are positive a/b = 5/2, and a/c [#permalink]
Show Tags
02 May 2017, 16:48
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
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: The integers a, b, and c are positive a/b = 5/2, and a/c
[#permalink]
02 May 2017, 16:48








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


7


If a, b, and c are integers and ab^2/c is a positive even in

Countdown 
6 
03 Apr 2017, 04:39 

19


If a, b, c and d are positive integers and a/b < c/d, which

stormbind 
9 
13 Sep 2016, 20:51 

4


If integers a,b,c are positive and a/b= 5/2 and a/c=7/5

jimmy86 
7 
04 Feb 2013, 04:42 

27


If a, b, and c are integers and a*b^2/c is a positive even

Orange08 
8 
20 Apr 2017, 16:43 

30


If a and b are positive integers such that ab and a/b are

twilight 
13 
14 Sep 2014, 15:39 



