Elizabeth is interested in dividing the rooms in the house among the f

Question

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.

A. 20; 8.
B. 30; 9.
C. 15; 6.
D. 10; 5.
E. 22; 10.

nikhilbansal08 · Answer

Scientists have found new evidence.

Let R be the initial number of rooms and F be the no of members

Then as per the given question : R+2 should be divisible by F-1..

Now check the given values and see which satisfy the above

Only two values satisfy the condition :

10, 5

30,9

10,5 can't be the solution as its already mentioned in statement that the initial no of room are not divisible by the initial no of family members .. hence answer is 30,9.... B

Nightfury14 · Answer

Option B) Initially 9 family members then reduced to 8 family members and Initially 30 rooms increased to 32 Rooms fits the requirement.

CounterSniper · Answer

clearly option B !!
30 + 2 and 9-1 
rooms = 32 and members =8
The rooms can now be divided among the members

Abhishek009 · Answer

One must try to solve such questions only by quick visual examination, which will reveal the answer in just 10 sec...

(B)  \frac{30 + 2}{9 - 1}  =  \frac{32}{8}  =  4

Thus, the correct answer must be (B) 30; 9

pushpitkc · Answer

For this question, the following two conditions must be satisfied
1. Add 2 to the current rooms & Reduce 1 from the initial number of members(Now Rooms/Members must be an integer)
2. Current Rooms/Members must not be an integer

Evaluating the answer options for the conditions
1. Both Options B and D are possible
2. All options possible except D

The answer option which satisfies both the conditions is  Option B

lor12345 · Answer

Hi!
Why D is incorrect?
10;5
10+2= 12
5-1=4
12/4=3

KarishmaB · Answer

Because we are given that the initial number of rooms cannot be divided equally among the number of family members.
But 10 is divisible by 5.

lor12345 · Answer

thank you! I missed that part!

JeffTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Elizabeth is interested in dividing the rooms in the house among the f

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Elizabeth is interested in dividing the rooms in the house among the f

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards