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

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Math Expert
Joined: 02 Sep 2009
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Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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13 Jul 2016, 01:55
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Difficulty:

35% (medium)

Question Stats:

69% (01:16) correct 31% (01:24) wrong based on 146 sessions

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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.

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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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13 Jul 2016, 03:11
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
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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13 Jul 2016, 04:07
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.

Option B) Initially 9 family members then reduced to 8 family members and Initially 30 rooms increased to 32 Rooms fits the requirement.
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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13 Jul 2016, 06:27
clearly option B !!
30 + 2 and 9-1
rooms = 32 and members =8
The rooms can now be divided among the members
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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25 Sep 2017, 08:39
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.

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

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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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25 Sep 2017, 09:24
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
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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09 Oct 2017, 03:26
Hi!
Why D is incorrect?
10;5
10+2= 12
5-1=4
12/4=3
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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09 Oct 2017, 03:38
lor12345 wrote:
Hi!
Why D is incorrect?
10;5
10+2= 12
5-1=4
12/4=3

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.
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Intern
Joined: 26 Sep 2017
Posts: 14
Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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09 Oct 2017, 04:23
VeritasPrepKarishma wrote:
lor12345 wrote:
Hi!
Why D is incorrect?
10;5
10+2= 12
5-1=4
12/4=3

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.

thank you! I missed that part!
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Re: Elizabeth is interested in dividing the rooms in the house among the f [#permalink]

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12 Oct 2017, 17:59
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.

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Re: Elizabeth is interested in dividing the rooms in the house among the f   [#permalink] 12 Oct 2017, 17:59
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