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got the least amount?

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by sanju09 » Mon Mar 26, 2012 12:55 am
$50000 are distributed among P, Q and R. Who got the least amount?
(1) P received one-fourth the amount that Q and R received together.
(2) R received what P and Q received together.
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by Anurag@Gurome » Mon Mar 26, 2012 1:17 am
sanju09 wrote:$50000 are distributed among P, Q and R. Who got the least amount?
(1) P received one-fourth the amount that Q and R received together.
(2) R received what P and Q received together.
Let us assume that P, Q, and R receive $x, $y, and $z respectively.
Then x + y + z = 50000

(1) P received one-fourth the amount that Q and R received together implies x = (y + z)/4; NOT sufficient.

(2) R received what P and Q received together implies z = x + y; NOT sufficient.

Combining (1) and (2), x = (y + x + y)/4 implies 4x = 2y + x or 3x = 2y
Also, x + y + z = 50000 and z = x + y implies 2x + 2y = 50000
We have 2 equations, 2 variables, which can be solved to find the least amount; SUFFICIENT.

The correct answer is C.
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