GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2019, 08:23

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
Joined: 12 Aug 2015
Posts: 280
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

Show Tags

New post 30 Jan 2016, 09:28
4
9
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

HideShow timer Statistics

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

_________________
KUDO me plenty
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4015
Location: Canada
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

Show Tags

New post 30 Jan 2016, 09:44
10
2
shasadou 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


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

Answer: E

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
_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Math Expert
avatar
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]

Show Tags

New post 30 Jan 2016, 09:50
4
shasadou 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..
_________________
Manager
Manager
avatar
G
Joined: 26 Dec 2015
Posts: 236
Location: United States (CA)
Concentration: Finance, Strategy
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]

Show Tags

New post 15 Jan 2017, 12:11
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
Director
avatar
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
Re: The sum of three integers A, B and C is 120. A is one third of the su  [#permalink]

Show Tags

New post 12 Apr 2017, 20:10
chetan2u wrote:
shasadou 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
Director
avatar
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]

Show Tags

New post 12 Apr 2017, 20:30
I don't understand the step where you isolate 40 and divide by 40?

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

Show Tags

New post 03 Feb 2019, 12:56
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
GMAT Club Bot
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
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne