Bunuel wrote:

Elizabeth is interested in dividing the rooms in the house among the family. Unfortunately, they do not divide equally. It turns out that in order for the rooms to be dividable, Elizabeth has to build two more rooms and kick out one of the family members. Which of the following can describe the number of the initial rooms in the house and the initial number of family members (in the order Rooms, family)?

A. 20; 8.

B. 30; 9.

C. 15; 6.

D. 10; 5.

E. 22; 10.

We can let r = the number of rooms and f = the number of family members; thus:

(r + 2)/(f - 1) = integer

So, we need to find the answer choice that when we add 2 to the number of rooms, subtract 1 from the number of family members, and then divide rooms by family members, we will get an integer.

We see that in answer choice B, (30 + 2)/(9 - 1) = 4; thus, we can have 30 initial rooms and 9 initial family members.

Note that answer choice D also satisfies (10 + 2)/(5 - 1) = integer, but if there were 10 rooms and 5 family members, it would have been possible to divide the rooms among the family without the need for additional rooms or kicking out family members, which is against the question stem.

Answer: B

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Jeffery Miller

Head of GMAT Instruction

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