|
Author |
Message |
|
TAGS:
|
|
|
Darden Thread Master
Joined: 04 Oct 2010
Posts: 60
GMAT 1: 720 Q48 V41
Followers: 3
Kudos [?]:
16
[0], given: 17
|
If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 [#permalink]
 03 Apr 2011, 08:04
Question Stats:
0% (00:00) correct
100% (01:36) wrong based on 0 sessions
Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?OPEN DISCUSSION OF THIS QUESTION IS HERE: the-integers-a-b-and-c-are-positive-a-b-5-2-and-a-c-128150.html
_________________
---
Jimmy
Life`s battles dont always go,
To the stronger or faster man;
But sooner or later the man who wins,
Is the man who THINKS HE CAN .
KUDOS me if you feel my contribution has helped you.
|
|
|
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
03 Apr 2011, 08:12
jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b ---1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Instructor
Joined: 24 Jun 2008
Posts: 973
Location: Toronto
Followers: 167
Kudos [?]:
443
[1] , given: 3
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
03 Apr 2011, 10:07
1
This post received
KUDOS
jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?When you have two positive integers a and b, and the ratio of a to b is 5 to 2, then a must always be a multiple of 5, and b must always be a multiple of 2. This will always be true when you have a ratio of two integers, provided the ratio is completely reduced (so if you knew, say, the ratio of a to b was 10 to 4, you'd need to reduce that ratio to 5 to 2 first before drawing any conclusions about multiples). So here, we know that the ratio of a to b is 5 to 2, so a is a multiple of 5. We also know the ratio of a to c is 7 to 5, so a is a multiple of 7. Thus a is a multiple of both 5 and 7, and the smallest possible value of a is 35. If a is 35, then since a/b = 5/2, b would be 14, and 2a + b = 84.
_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1721
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
228
[1] , given: 34
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
03 Apr 2011, 19:02
1
This post received
KUDOS
We can see that : a:b:c = 35:14:10 because a has 7 and 5 as factors, so least value of a = 35, and hence b = 14 ( and c = 25) So 2a + b = 70 + 14 = 84
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 11 Dec 2010
Posts: 113
WE: Consulting (Consulting)
Followers: 4
Kudos [?]:
16
[0], given: 48
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
03 Apr 2011, 22:09
a:b = 5:2
a:c = 7:5
So to form a:b:c we a needs to be the LCM of 7 and 5 i.e. 35
So Multiply first ratio by 7 and second by 5
a:b:c = 35:14:25
So 2*35+14 = 84
|
|
|
|
|
|
Darden Thread Master
Joined: 04 Oct 2010
Posts: 60
GMAT 1: 720 Q48 V41
Followers: 3
Kudos [?]:
16
[0], given: 17
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
04 Apr 2011, 01:26
thanks everyone.... Specially liked Ian`s explanation....the answer is a lot simpler than i thought....
_________________
---
Jimmy
Life`s battles dont always go,
To the stronger or faster man;
But sooner or later the man who wins,
Is the man who THINKS HE CAN .
KUDOS me if you feel my contribution has helped you.
|
|
|
|
|
|
Intern
Joined: 23 Dec 2012
Posts: 4
Followers: 0
Kudos [?]:
1
[0], given: 0
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
02 Feb 2013, 17:19
fluke wrote: jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b ---1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84. -------------------------------------------------------------------------------------------------------------------------------------------- Hey Fluke, Can you please explain me where my method went wrong. a/b=5/2---> a=2.5*b a/c=7/5--->a=1.4*C 2.5*b = 1.4*c c=1.8*b As B and C have to be integers, the least integer value for B that would make C an integer is '5'. From the stem, we know that 2a=5b 2a+b=5b+b=6b As we know that b=5. 6b=30.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11565
Followers: 1796
Kudos [?]:
9570
[0], given: 826
|
Re: PS : Algebra/Ratio - High Difficulty [#permalink]
04 Feb 2013, 04:42
ulabrevolution wrote: fluke wrote: jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b ---1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84. -------------------------------------------------------------------------------------------------------------------------------------------- Hey Fluke, Can you please explain me where my method went wrong. a/b=5/2---> a=2.5*b a/c=7/5--->a=1.4*C 2.5*b = 1.4*c c=1.8*bAs B and C have to be integers, the least integer value for B that would make C an integer is '5'. From the stem, we know that 2a=5b 2a+b=5b+b=6b As we know that b=5. 6b=30. From 2.5b=1.4c it follows that c=25/14*b. Now, 25/14 does not equal to 1.8. OPEN DISCUSSION OF THIS QUESTION IS HERE: the-integers-a-b-and-c-are-positive-a-b-5-2-and-a-c-128150.html
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: PS : Algebra/Ratio - High Difficulty
[#permalink]
04 Feb 2013, 04:42
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If a and b are positive integers such that a-b and a/b
|
andy1979 |
6 |
04 Jul 2005, 03:34 |
|
|
|
|
a,b,c and d are positive integers such that ab=24, cd=48,
|
kevincan |
3 |
12 Aug 2006, 11:12 |
 |
|
|
a,b and c are positive integers such that abc= 450 and
|
kevincan |
14 |
18 Sep 2006, 01:42 |
|
|
1
|
|
If a,b,c and d are positive integers, is (a/b) (c/d) >
|
amitjash |
4 |
01 Aug 2010, 22:11 |
|
|
|
 |
The integers a, b, and c are positive a/b = 5/2, and a/c
|
Chembeti |
7 |
26 Feb 2012, 00:21 |
|
|
|
|
|
|
close
