Author
Message
TAGS:
Darden Thread Master

Joined: 04 Oct 2010

Posts: 60

GMAT 1 : 720 Q48 V41

Followers: 3

Kudos [? ]:
19
[0 ] , given: 17

If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 [#permalink ]
03 Apr 2011, 07:04

Question Stats:

0% (00:00) correct

100% (01:36) wrong

based on 6 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: 2047

Followers: 128

Kudos [? ]:
926
[0 ] , given: 376

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
03 Apr 2011, 07:12

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.

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

GMAT Instructor

Joined: 24 Jun 2008

Posts: 967

Location: Toronto

Followers: 256

Kudos [? ]:
681
[2 ] , given: 3

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
03 Apr 2011, 09:07
2

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: 1691

Location: United States (IN)

Concentration: Strategy, Technology

Followers: 30

Kudos [? ]:
290
[1 ] , given: 36

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
03 Apr 2011, 18:02
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)Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager

Joined: 11 Dec 2010

Posts: 115

WE: Consulting (Consulting)

Followers: 4

Kudos [? ]:
23
[0 ] , given: 50

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
03 Apr 2011, 21:09

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 [? ]:
19
[0 ] , given: 17

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
04 Apr 2011, 00:26

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, 16:19

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.

Math Expert

Joined: 02 Sep 2009

Posts: 23482

Followers: 3501

Kudos [? ]:
26447
[0 ] , given: 2712

Re: PS : Algebra/Ratio - High Difficulty [#permalink ]
04 Feb 2013, 03:42
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*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.

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 _________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! 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 ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: PS : Algebra/Ratio - High Difficulty
[#permalink ]
04 Feb 2013, 03:42

Similar topics
Author
Replies
Last post
Similar Topics:

2
The integers a, b, and c are positive a/b = 5/2, and a/c
Chembeti
9
25 Feb 2012, 23:21

1
If a,b,c and d are positive integers, is (a/b) (c/d) >
amitjash
4
01 Aug 2010, 21:11

a,b and c are positive integers such that abc= 450 and
kevincan
14
18 Sep 2006, 00:42

a,b,c and d are positive integers such that ab=24, cd=48,
kevincan
3
12 Aug 2006, 10:12

If a and b are positive integers such that a-b and a/b
andy1979
6
04 Jul 2005, 02:34