On June 1, Mary paid Omar $360 for rent and utilities for the month of

We need the amount of utilities money refunded to Mary. For that we need to know two thing : how much did she pay for utilities (out of the total 360) and for how many days she stayed in June.

(1) Mary moved out on June 24.
Tells us for how many days she stayed in June. Doesn't tell us the utilities amount.

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

Tells us that utilities amount was < (1/5) Rent amount.

Rent + Utilities = 360
Rent + (Something less than Rent/5) = 360

Now, if Rent were 300, utilities would be 60 (exactly 1/5th of rent). So we know that rent > 300 and utilities < 60. But we don't get an exact value for utilities.

Using both statements, we don't have an exact value for amount of utilities. Hence answer (E)

Responding to a pm:


This is not how it can be inferred. It should be

Utilities < Rent/5

(1) Mary moved out on June 24.
Clearly insufficient as it does not tell how many portions of 360 were for utilities
(2) The amount Mary paid for utilities was less than 1/5 the amount Mary paid for rent.
Insufficient as it does not tell when did Mary move out
Combining statement 1 and 2
Let rent be x so utilities will be less than x/5.
x+ x/5= 360
hence utilities will be 60 for the whole month. for 6 days to refund it will be less than 12 $ but we don't exactly what less than 12$.
Hence E insufficient.
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For the month of June, Rent & Utilities of $360 is paid by Mary to Omar. A refund is
given because Mary does not stay for the entire month.

(1) Mary moved out on June 24.
This shows that she was not occupying the house for 6 days in the month of June.
However, this information is not enough to find the exact amount of the refund (Insufficient)

(2) The amount Mary paid for utilities was less than 1/5 the amount Mary paid for rent.
We know that the amount Mary paid for utilities was LESS than \(\frac{1}{5}\)th the amount she
paid for rent. However, since we aren't given by exactly how much the cost of utilities is
less than the cost for the rent, we can't find the exact amount of the refund. (Insufficient)

Even with the combination statement, we cannot clearly assess the exact refund which
was returned to Mary(since we aren't given an exact ratio of cost of utilities to rent (Insufficient - Option E)

Solution

Given:

• 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

To find:

• The amount (in dollars) that Omar refunded to Mary

Analysing Statement 1

• As per the information given in statement 1, Mary moved out on June 24.

o We can only say Mary didn’t occupy the room for the last 6 days of the month of June
o But we cannot find out the refund amount as we don’t know what amount was allocated, out of $360, towards rent and utilities individually

Hence, statement 1 is not sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, the amount Mary paid for utilities was less than \(\frac{1}{5}\) the amount Mary paid for rent

o If Mary paid x as rent, then we can say the amount paid for utilities was less than \(\frac{x}{5}\)
o However, the exact less amount cannot be found out, neither the rent amount

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Even after combining the statements, we cannot find out the exact rent amount or the proportion of the total $360

Hence, the correct answer is option E.

Answer: E
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Mary paid $360 for rent & utilities, let consider P(utilities)+P(rent)=$360
for moving out early, how much was the return amount in utilities??
to find out, we need information on which date she moved out & what was the amount she paid for utilities in $360.

a) only information on date & no information on price. Not sufficient (cancel AD)
b)cost paid for utilities < 1/5*cost paid for rent. No information on date & actual price. Not sufficient ( cancel B)

Together a&b, date information added but still no information on paid amount. Not sufficient ( Cancel C)

Answer E

The quickest way to solve this is to observe the detail in the statement.

She paid LESS THAN some amount

no matter what - we can NEVER get a value from this - because we can't get a VALUE therefore E is the answer - no need to do too much thinking on this.

Remember GMAT is a test of reasoning.

After Combining both the statements we come to know that price of utilities are 60$.
so for a single day the price of utility would be (60/30)=2
then she got the money for last 6 days i.e 6*2=12.

Please clarify.
Thanks

Answer: Option E

Video solution by GMATinsight



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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

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