Is x% of x% of y equal to x% less than y ?

[Makushr1]

From MGMAT CAT2

Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1

OA: A

[4GMAT_Mumbai]

Hi,

Statement 1

(x^2 + 100x)/10000 = 1

(x^2 / 10000) + (x/100) = 1

(x^2 / 10000) = 1 - (x/100)

Multiply by y on both sides,

(x^2 / 10000) y = y - y (x/100)

(x / 100) (x/100) y = y - y (x/100)

x% of x% of y = x% less than y.

Hence, 1 is suff

Statement 2:

y^2 +y - 1 = 0

y = (-1 +/- root(5)) / 2

If x = 10%; x% of x% of y = 1% of y
x% less than y = 99% of y. Hence not equal.

But, there will be some value of x% (little more than 60%) at which x% of x% of y is indeed equal to x% less than y.

Hence, 2 is insufficient.

Hope this helps. Thanks.