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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