GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Aug 2020, 07:55 ### 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

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.  # If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65763
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

2
9 00:00

Difficulty:   35% (medium)

Question Stats: 70% (02:06) correct 30% (02:34) wrong based on 332 sessions

### HideShow timer Statistics

If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

_________________
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3440
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

10
1
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

Hey,

Though there are a number of ways to solve this. I would like to use a slightly different method which involved options elimination, using the concept of even-odd.

We are given that a+b = 2c, now 2c is EVEN, therefore the sum of a + b should also be EVEN.

Look at the answer choices and focus on only the first two numbers and their sum -

A. $$1+2 = 3$$ - ODD
B. $$1 + 3 = 4$$- EVEN
C. $$3+ 2 = 5$$ - ODD
D. $$1+ 4 =5$$ - ODD
E.$$1+2 =3$$ - ODD

Hence Option B is the correct answer. It is always a good idea to look for patterns in the options if one is not sure how to approach using the conventional method. Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  _________________
##### General Discussion
Intern  B
Joined: 08 Sep 2016
Posts: 34
Location: Georgia
GPA: 3.75
WE: Analyst (Investment Banking)
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

3
a+b+c = 3c
a+5a=3c
6a=3c
2a=c

from substitue:

a+2a=b
3a=b

so ratio will be 1:3:2

Manager  S
Joined: 26 Jun 2014
Posts: 75
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

1
giobas wrote:
a+b+c = 3c
a+5a=3c
6a=3c
2a=c

from substitue:

a+2a=b
3a=b

so ratio will be 1:3:2

Nice way of solving it.. I couldn't. I had to back test the options one by one
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 5033
Location: India
GPA: 3.5
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

JamieCecil wrote:
Nice way of solving it.. I couldn't. I had to back test the options one by one

I will consider that as an effective way of solving this question , I do the same as well...

Check using the options..

For option (B) -

a = 1
b = 3
c = 2

a + b = 2c Or, 1 + 3 = 2*2 ( Satisfies )
a + c = b , Or, 1 + 2 = 3 ( Satisfies )
b + c = 5a, Or 3 + 2 = 5*1 ( Satisfies )

Check using other options, none except (B) satisfies, hence thats the correct answer...

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  S
Joined: 24 Oct 2016
Posts: 238
Location: India
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

in such kind of problems its easy to back solving it if we plug answers then the only values which satisfy is 1:3:2 which option B
Manager  G
Joined: 02 Aug 2015
Posts: 151
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

I think the sum can be solved just by scanning the options.

Given a+c =b, two inferences can be made from this option.
1. If all three numbers are negative, b has to be the smallest. None of the ratios in the options have b as the smallest. So the numbers are positive.
2. Since the numbers are positive, b is the largest among a,b, and c. So options A,C, and E can be eliminated as b is not the biggest in them.

Option D says the b is twice that of c. If that's the case then from 1st equation a=2c-b will be 0 so the ratio will fall.

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

1
1
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

We are given that:

a + b = 2c

a + c = b

b + c = 5a

Subtracting the second equation from the first equation, we have:

(a + b = 2c) - (a + c = b)

b - c = 2c - b

2b = 3c

Subtracting the third equation from the second equation, we have:

(a + c = b) - (b + c = 5a)

a - b = b - 5a

6a = 2b

Since 2b = 3c and 2b = 6a, we can say that 6a = 2b = 3c

Furthermore, we see that 6a = 2b = 3c holds when a = 1, b = 3, and c = 2.

Thus, the ratio of a to b to c = 1 to 3 to 2.

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Manager  S
Joined: 18 Oct 2016
Posts: 127
Location: India
WE: Engineering (Energy and Utilities)
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

Option B

Correct ratio should give a + b as Even (Using eq.n I)

"Alternatively"

Correct ratio should satisfy all 3 equations.

E.g., a + b =2c : 1+3 = 2*2 For B).
Director  S
Joined: 12 Nov 2016
Posts: 663
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

1
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

You don't necessarily even have to substitute- just plug in a value for a b and c that works and then you have a ratio; for example, consider a = 1, b = 3 , c = 2

1 + 3 = 2(2)

Albeit, it is still important to know how to substitute values into equations which I think is the concept being tested. Learn the rules only to break them when convenient.
Manager  S
Joined: 14 Sep 2016
Posts: 58
Concentration: Finance, Economics
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

1
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

a+c=b gives the answer away without any math.
This means that b is largest.
The only answers with b being the largest are B & D.
Looking at B you can cleary see that 1+2=3 or a+c=b

Originally posted by IdiomSavant on 24 Apr 2017, 12:23.
Last edited by IdiomSavant on 25 Apr 2017, 05:32, edited 2 times in total.
Director  S
Joined: 12 Nov 2016
Posts: 663
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

IdiomSavant wrote:
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

a+c=b gives the answer away without any math.
This means that b is largest.
The only answers with b being the largest are B & D.
Looking at B you can clear see that 1&2=3 or a+c=b

That's kind what I thought too
Intern  S
Joined: 13 Dec 2016
Posts: 38
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

Abhishek009 : I tried solving it the traditional way and it took me a considerable amount of time. I liked your method of plugging in nos. from the options given. I wanted to check if it will be fairly OK to just check any one of the three equations as long as only one option gives positive result for that equation and move on without checking the answer choices for the remaining equations ?
Senior SC Moderator V
Joined: 22 May 2016
Posts: 4002
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

Here, I used only two of the three equations, avoiding b + c = 5a entirely.

b is the only variable with coefficient 1 in all three equations.

1. With b as initial focus, rewrite a + c = b ----> b = a + c

2. Two equations to choose from now: a + b = 2c and b + c = 5a.

Coefficient 2 looked easier than coefficient 5. So I substituted value of b into a + b = 2c ---->

a + (a + c) = 2c, subtract c from both sides to get

2a = c or c = 2a

3. c now has a coefficient of 1, and b has a coefficient of 1 in equation from Step 1: b = a + c, substitute c = 2a ------> b = a + 2a, b = 3a

4. b and c are now both written in terms of a, thus

a = 1a
b = 3a
c = 2a.

Ratio of a:b:c is therefore 1:3:2

_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
Manager  G
Joined: 29 May 2017
Posts: 120
Location: United States (AL)
GMAT 1: 760 Q50 V42 Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

My solution is as follows:

try to see the equations and find out which is the largest among a, b, c; clearly by equation 2 we can say b is the largest.
only two options have b as the largest, plug one into the the set of equations, if it passes great! else the other is the answer.!
Senior Manager  S
Joined: 15 Dec 2016
Posts: 253
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

Hey,

Though there are a number of ways to solve this. I would like to use a slightly different method which involved options elimination, using the concept of even-odd.

We are given that a+b = 2c, now 2c is EVEN, therefore the sum of a + b should also be EVEN.

Look at the answer choices and focus on only the first two numbers and their sum -

A. $$1+2 = 3$$ - ODD
B. $$1 + 3 = 4$$- EVEN
C. $$3+ 2 = 5$$ - ODD
D. $$1+ 4 =5$$ - ODD
E.$$1+2 =3$$ - ODD

Hence Option B is the correct answer. It is always a good idea to look for patterns in the options if one is not sure how to approach using the conventional method. Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  Hello EgmatQuantExpert Bunuel - follow up on this method of doing the problem VeritasKarishma

I understand a + b has to be an even multiple of 2

Question : in all the answer choices, its quite possible that the unknown multiplier in all the options are even

Option 1) is 1: 2 :3

Assuming an even multiplier, lets say k = 6, thus the actual values are 6 : 12 : 18

Hence a + b in this ratio is also even (i.e. 6 + 12 = 18)

Why is this not a scenario / option we need to look at.

Thank you !
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?  [#permalink]

### Show Tags

jabhatta@umail.iu.edu wrote:
EgmatQuantExpert wrote:
Bunuel wrote:
If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?

A. 1:2:3
B. 1:3:2
C. 3:2:1
D. 1:4:2
E. 1:2:5

Hey,

Though there are a number of ways to solve this. I would like to use a slightly different method which involved options elimination, using the concept of even-odd.

We are given that a+b = 2c, now 2c is EVEN, therefore the sum of a + b should also be EVEN.

Look at the answer choices and focus on only the first two numbers and their sum -

A. $$1+2 = 3$$ - ODD
B. $$1 + 3 = 4$$- EVEN
C. $$3+ 2 = 5$$ - ODD
D. $$1+ 4 =5$$ - ODD
E.$$1+2 =3$$ - ODD

Hence Option B is the correct answer. It is always a good idea to look for patterns in the options if one is not sure how to approach using the conventional method. Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  Hello EgmatQuantExpert Bunuel - follow up on this method of doing the problem VeritasKarishma

I understand a + b has to be an even multiple of 2

Question : in all the answer choices, its quite possible that the unknown multiplier in all the options are even

Option 1) is 1: 2 :3

Assuming an even multiplier, lets say k = 6, thus the actual values are 6 : 12 : 18

Hence a + b in this ratio is also even (i.e. 6 + 12 = 18)

Why is this not a scenario / option we need to look at.

Thank you !

Yes, you are right. If the multiplier is even, though the sum of ratio terms may not be even, the actual sum may be even.
Instead I would use the knowledge that the addition relation of actual variables holds in case of ratios too.
i.e. if actually a + b = 2c, then even in ratio terms, a + b will be equal to 2c.

Since 1 + 2 is not equal to 2*3, this is not correct.

Only for option (B), 1 + 3 = 2*2

Note why this is so. We routinely use the ratio scale and actual value scale while using ratios as discussed here:
https://www.veritasprep.com/blog/2011/0 ... of-ratios/

Let's say we have the ratio a:b:c = 1:3:2
Then, a = k, b = 3k and c = 2k

Then an addition relation such as a + b = 2c becomes
k + 3k = 2 * 2k
k(1 + 3) = 2 * 2k
(1 + 3) = 2*2

Since we can take the common multiplier out, the same relation will hold in terms of ratios too.
_________________
Karishma
Veritas Prep GMAT Instructor Re: If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?   [#permalink] 09 Jul 2020, 23:19

# If a+b=2c, a+c=b, and b+c=5a, what is the ratio of a:b:c?   