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GMAT - Data Sufficiency - Percentage

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 ? (more)

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.

Assume the original price per share of stock X was x and of stock Y was y

final price of X = x + 10% of x = 1.1x

final price of Y = y - 10% of y = 0.9y

% required = final price of Y * 100 / original price of X = 0.9*100y/x = 90 y/x

we need the value of y/x

Statement 1:

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

increase in price per share of X = 1.1x - x = 0.1x

thus y = 0.1x 

y/x = 0.1

Sufficient

 

Statement 2:

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

increase in price of Stock X = 0.1x

decrease in price of Stock Y = y - 0.9y = 0.1y

Statement 2 says

10/11 * 0.1y = 0.1x

y/x = 11/10

Sufficient

 

Is the number of members of Club X greater than the number of members of Club Y ? (more)

Is the number of members of Club X greater than the number of members of Club Y ?

Statement 1

Of the members of Club X, 20 percent are also members of Club Y. 
 

Statement 2

Of the members of Club Y, 30 percent are also members of Club X.
 

Yes