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 120We 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 + CThere 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/969Cheers,

Brent

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