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

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

The OA is E

Source: Official Guide

Say the rent for the month of June is $X and charges for the utility per day is $y. Thus, we have

Say Mary moves out after d days, where d < 30; we know that June is a 30 days month.

We have to find out the value of $(30 - d)y.

Let's take each statement one by one.

1) Mary moves out on June 24.

=> Money to be refunded = $(30 - d)y = $(30 - 24)y = $6y.

Since we do not know the value of y, we can get the correct answer. Insufficient.

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

=> dy < X/5. Insufficient.

(1) and (2) together

From 2, dy < X/5, we have 30y < X/5 => y < X/150

From X + 30y = 360, we have X + 30*(X/150) < 360 => X + X/5 < 360 => 6X/5 < 360 => X < 300. Since the value of X is not known, we can't have a unique value of y. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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swerve wrote: ↑

Wed Dec 26, 2018 10:41 am

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

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

The OA is E

Source: Official Guide

Solution:

We need to determine the amount of money, in dollars, Omar refunded to Mary.

Statement One Alone:

Since Mary moved out on June 24, she should be refunded for the 6 remaining unused days of June in utilities, i.e., 6/30 = 1/5 of June’s utilities she has paid. However, since we only know the total amount Mary paid for rent and utilities, but not the actual amount of either expense, we can’t determine the amount of the refund. Statement one alone is not sufficient.

Statement Two Alone:

With statement two, since we still can’t determine the actual amount of either expense, we can’t determine the amount of the refund. Statement two is not sufficient.

Statements One and Two Together:

Even with the two statements, we still can’t determine the actual amount of each of the two expenses, so we can’t determine the amount of the refund. For example, if the utilities were $50 and the rent was $310 (notice that $50 is less than 1/5 of $310), then the refund should be 1/5 x 50 = $10. However, if the utilities were $40 and the rent was $320 (notice that $40 is less than 1/5 of $320), then the refund should be 1/5 x 40 = $8. Both statements together are not sufficient.

Answer: E