Data Sufficiency

AAPL wrote:GMAT Paper Tests

How many more men than women are in the room?

1) There is a total of 20 women and men in the room.
2) The number of men in the room equals the square of the number of women in the room.

OA C

Say the number of men = x and the number of women = y;

We have to get the value of x - y.

Let's take each statement one by one.

1) There is a total of 20 women and men in the room.

x + y = 20 ---(1)

Can't get x - y. Insufficient.

2) The number of men in the room equals the square of the number of women in the room.

=> x = y^2 ---(2)

Can't get x - y. Insufficient.

(1) and (2) together

From (1) and (2), we have

y^2 + y = 20

y^2 + y - 20 = 0

y^2 + 5y - 4y - 20 =0

y(y + 5) - 4(y + 5) = 0

(y - 4)(y + 5) = 0

y = 4 or - 5

Since y is a positive integer, y = 4; thus, x = y^2 = 4^2 = 16 => x - y = 16 - 4 = 12. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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