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What is the average of A, B, and C?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Oct 26, 2017 6:45 am
LUANDATO wrote:What is the average of A, B, and C?

(1) 3A + B + 2C = 17

(2) 0.5A + B + 0.75C = 7

The OA is C.

I need help with this DS question. Can any expert explain it for me please? Thanks.
Clearly, no statement alone is sufficient.

(1) and (2) combined:

We have 3A + B + 2C = 17 ---(1) and

0.5A + B + 0.75C = 7 ---(2)

Multiplying equation (2) by 4, we get 4 x (0.5A + B + 0.75C = 7) => 2A + 4B + 3C = 28 ---(3)

Adding eqn (1) and (3), we get

(3A + B + 2C = 17) + (2A + 4B + 3C = 28)

=> 5A + 5B + 5C = 45

A + B + C = 9 => Average = (A + B + C)/3 = 3. Sufficient

The correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay

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