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Senior Manager  Joined: 12 Aug 2015
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Concentration: General Management, Operations
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WE: Management Consulting (Consulting)
The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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Question Stats: 77% (02:27) correct 23% (03:07) wrong based on 375 sessions

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The sum of three integers A, B and C is 120. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?

A. 20
B. 30
C. 45
D. 50
E. 70

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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The sum of three integers A, B and C is 120. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?

A. 20
B. 30
C. 45
D. 50
E. 70

The sum of three integers A, B and C is 120
We can write: A + B + C = 120

A is one third of the sum of B and C
We can write: A = (1/3)(B + C)
Multiply both sides by 3 to get: 3A = B + C

B is one fifth of the sum of A and C.
We can write: B = (1/5)(A + C)
Multiply both sides by 5 to get: 5B = A + C

There are MANY different ways to solve this system of 3 equations.
Here's ONE solution.

Take A + B + C = 120 and replace B + C with 3A to get: A + 3A = 120
Solve to get A = 30

Take A + B + C = 120 and replace A + C with 5B to get: B + 5B = 120
Solve to get B = 20

Now that we now A = 30, and B = 20, AND we know that A + B + C = 120, we can conclude that C = 70

For more info on solving a system of 3 equations and 3 unknowns, see this free video: http://www.gmatprepnow.com/module/gmat- ... /video/969

Cheers,
Brent
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Math Expert V
Joined: 02 Aug 2009
Posts: 8005
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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The sum of three integers A, B and C is 120. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?

A. 20
B. 30
C. 45
D. 50
E. 70

Hi,
FROM:-
1) A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=120..
so 1/3(B+C)+B+C=120..
B+C=120*3/4=90...
A=120-90=30

2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=120..
so 1/5(A+C)+A+C=120..
A+C=120*5/6=100...

but A=30, so C=100-30=70..
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WE: Investment Banking (Venture Capital)
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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This is what I did:

Given: (I) A+B+C=120; (II) A=1/3(B+C); (III) B=1/5(A+C)

Recognize:
- You can rewrite (I) as: A=120-B-C. Therefore, set both equations equal to each other: 1/3(B+C)=120-B-C --> (1/3)B+(1/3)C=120-B-C. Isolate 120 --> (4/3)B+(4/3)C=120. --> (4/3)B+C=120 --> 4(B+C)=360. --> B+C=90

- Same method above applied to B. --> B=120-A-C. (1/5)A+C=120-A-C --> (6/5)A+C=120. A+C=100.

NOW:
A+B+C=120.
B+C=90
A+C=100.

Plug in A/C:
E) C=70. Means that: B=20, A=30.
- Check: A+B+C=120. Correct.
Director  S
Joined: 12 Nov 2016
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Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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chetan2u wrote:
The sum of three integers A, B and C is 120. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?

A. 20
B. 30
C. 45
D. 50
E. 70

Hi,
FROM:-
1) A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=120..
so 1/3(B+C)+B+C=120..
B+C=120*3/4=90...
A=120-90=30

2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=120..
so 1/5(A+C)+A+C=120..
A+C=120*5/6=100...

but A=30, so C=100-30=70..

Thank you for the solution- this is very clear
Director  S
Joined: 12 Nov 2016
Posts: 699
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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I don't understand the step where you isolate 40 and divide by 40?

Nevermind- just needed to drill into the question deeper.
Intern  B
Joined: 03 Jan 2017
Posts: 21
Location: India
Concentration: Finance, Economics
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

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The quicker way:

A=1/3(B+C)
B+C=3A
Substituting the value of B+C in Equation A+B+C=120
A+3A=120===> A=30

B=1/5(A+C)
A+C=5B
Substituting the value of A+C in Equation A+B+C=120
5B+B=120===> B=20

To find C, substitue the value of A and B in the equation A+B+C=120
30+20+C=120===> C=70

Ans: E Re: The sum of three integers A, B and C is 120. A is one third of the su   [#permalink] 03 Feb 2019, 12:56
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