Data Sufficiency

BTGmoderatorDC wrote:On June 1, Mary paid Omar $360 for rent and utilities for the month of June. Mary moved out early, and Omar refunded the money she paid for utilities, but not for rent, for the days in June after she moved out. How many dollars did Omar refund to Mary?

(1) Mary moved out on June 24.
(2) The amount Mary paid for utilities was less than 1/5 the amount Mary paid for rent.

Given: Amount paid in June for Rent + Utilities = $360

We have to find out the money Omar refund to Mary.

Let the fixed per month rent be $x and the per day utilities be $y per day.

Thus, x + 30y = 360

Let's take each statement one by one.

(1) Mary moved out on June 24.

The amount refunded would be $6y (June is out 30 days and she moved out on June 24), but we can't get the value of y. Insufficient.

(2) The amount Mary paid for utilities was less than 1/5 the amount Mary paid for rent.

=> 30y < x/5

150y < x. Can't get the unique value of y. Insufficient.

(1) and (2) together

Even after combining the equation (x + 30y = 360) and the inequality (150y < x), we can't get the value of $6y. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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