Data Sufficiency

tonebeeze wrote:I got the problem correct. I just want to make sure my algebra translations are on point. Can someone please walk me through the algebra? Thanks!

The price per share of stock X increased by 10 percent over the same time period that the price per share of stock Y decreased by 10 percent. The reduced price per share of stock Y was what percent of the original price per share of stock X?

1. The increased price per share of stock X was equal to the original price per share of stock Y.

2. The increase in the price per share of stock X was 10/11 the decrease in the price per share of stock Y.

OA = D

Let the original price per share of stock X = $x and the original price per share of stock Y = $y
The price per share of stock X increased by 10 percent, then the increased price per share of stock X = x + 10% 0f x = x + 0.1x = 1.1x
The price per share of stock Y decreased by 10 percent, then the reduced price per share of stock Y = y - 10% 0f y = y - 0.1y = 0.9y
Let the reduced price per share of stock Y is N% of the original price per share of stock X.
Then 0.9y = (N/100) of x implies N = 90y/x.
We need the value of y/x to find the value of N.

(1) 1.1x = y implies y/x = 1.1. Hence, SUFFICIENT.

(2) 0.1x = (10/11)0.1y. Again we can get the value of y/x from this equation. So, again (2) is SUFFICIENT.

The correct answer is D.