Data Sufficiency

Princeton Review

Just before Christmas stereo \(x\) and stereo \(y\) both go on sale. If for the sale, both stereos are discounted from their regular prices, is the Christmas sale price of stereo \(x\) lower than the Christmas sale price of stereo \(y\)?

1. The sale price of stereo \(x\) is 15 percent less than its regular price; the sale price of stereo \(y\) is 20 percent less than its regular price.

2. The sale price of stereo \(x\) is $150 less than its regular price; the sale price of stereo \(y\) is $200 less than its regular price.

OA C

Question => Is the Christmas sale price of stereo x lower than the Christmas sale price of stereo y.
Let regular price of stereo x = x
Let regular price of stereo y = y
Statement 1 => The sale price of stereo x is 15% less than its regular price; the sale price of stereo y is 20% less than its regular price
x - ( 15% * x ) and y - ( 20% xy) but the value of x and y ( i.e regular price ) is unknown hence statement 1 is NOT SUFFICIENT
Statement 2 => The sale price of stereo x is $150 less than it's regular price; the sale price of stereo y is $200 less than its regular price
x - 150 and y - 200 but the value of x and y ( i.e regular price is unknown ) hence, statement 2 is NOT SUFFICIENT
Combining both statement together =>
$$\frac{\left(Discount\ amount\right)}{original\ amount}=discount\ percentage$$
$$\frac{x-150}{x}=15\%$$ $$\frac{x-150}{x}=\frac{15}{100}=>176$$
$$Also,\ \frac{\ y-200}{y}=20\%;\ =>\ \frac{y-200}{y}=\frac{20}{100}=250$$
Both statements together are SUFFICIENT

Answer is therefore Option C