On Friday morning at a particular hotel, 5/9 of the rooms were cleaned in preparation for weekend visitors. Of the rooms

[BTGmoderatorDC]

On Friday morning at a particular hotel, 5/9 of the rooms were cleaned in preparation for weekend visitors. Of the rooms that were not cleaned, 1/3 were planned to be vacant for the weekend and therefore did not need to be cleaned. Of the rooms that needed to be cleaned but were not, the staff was able on Friday afternoon to clean 3/5 before check-in time. What fraction of the hotel's rooms were cleaned on Friday before check-in time?

A. 11/15
B. 7/9
C. 37/45
D. 13/15
E. 8/9


OA A

Source: Veritas Prep

[Jay@ManhattanReview]

On Friday morning at a particular hotel, 5/9 of the rooms were cleaned in preparation for weekend visitors. Of the rooms that were not cleaned, 1/3 were planned to be vacant for the weekend and therefore did not need to be cleaned. Of the rooms that needed to be cleaned but were not, the staff was able on Friday afternoon to clean 3/5 before check-in time. What fraction of the hotel's rooms were cleaned on Friday before check-in time?

A. 11/15
B. 7/9
C. 37/45
D. 13/15
E. 8/9

OA A

Source: Veritas Prep

• Fraction of rooms cleaned on Friday morning = 5/9 ---(1);

• Fraction of rooms remaining to be cleaned = 1 – 5/9 = 4/9

• Fraction of rooms not to be cleaned = 1/3 of 4/9 = 4/27

• Fraction of rooms of the remaining rooms to be cleaned on Friday evening = 3/5 of 2/3 of 4/9 = 8/45 ---(2)

• Fraction of rooms cleaned on Friday = 5/9 + 8/45 = 11/15

The correct answer: A

Hope this helps!

-Jay
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Manhattan Review

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[Scott@TargetTestPrep]

On Friday morning at a particular hotel, 5/9 of the rooms were cleaned in preparation for weekend visitors. Of the rooms that were not cleaned, 1/3 were planned to be vacant for the weekend and therefore did not need to be cleaned. Of the rooms that needed to be cleaned but were not, the staff was able on Friday afternoon to clean 3/5 before check-in time. What fraction of the hotel's rooms were cleaned on Friday before check-in time?

A. 11/15
B. 7/9
C. 37/45
D. 13/15
E. 8/9


OA A

Source: Veritas Prep

We can let the total number of rooms in the hotel = 270. Thus, 5/9 x 270 = 150 rooms were cleaned on Friday morning, and 120 rooms were not. Since 1/3 x 120 = 40 rooms did not need to be cleaned, 80 rooms needed to be cleaned. Since 3/5 x 80 = 48 rooms were cleaned on Friday afternoon, a total of 150 + 48 = 198 rooms were cleaned on Friday. Therefore, the fraction of rooms cleaned before check-in time was 198/270 = 22/30 = 11/15.

Answer: A