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
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
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.
