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The total cost of a vacation was divided among 3 people. If

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The total cost of a vacation was divided among 3 people. If [#permalink]

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New post Updated on: 26 Jul 2014, 16:17
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The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600
[Reveal] Spoiler: OA

Originally posted by blog on 31 Jan 2008, 20:00.
Last edited by Bunuel on 26 Jul 2014, 16:17, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: The total cost of a vacation was divided among 3 people. If [#permalink]

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New post 31 Jan 2008, 21:33
blog wrote:
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?

1. $200
2. $300
3. $400
4. $500
5. $600


x/3=c x/4=c-50 ---> x/4=x/3-50 ---> x/4-x/3=-50 --> -x/12=-50 --> x=600


E
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Re: The total cost of a vacation was divided among 3 people. If [#permalink]

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New post 31 Jan 2008, 21:45
x/4=x/3-50 where x is total cost of vacation

x=600
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Re: The total cost of a vacation was divided among 3 people. If [#permalink]

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New post 16 Jan 2016, 07:23
C for cost.
P price per person.
C= 3*P
C-200=4*P

Substituting the value of P from the first equation onto the second we get P = 200.
Plugging in the value of P in the first equation, we get C= 600. Which leads us to answer choice E
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Re: The total cost of a vacation was divided among 3 people. If [#permalink]

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New post 17 Jan 2016, 21:17
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Hi All,

This question can be solved by TESTing THE ANSWERS. There are also some logical 'shortcuts' in the design of this question that you can take advantage of.

We're told that the total cost of a vacation was divided among 3 PEOPLE. We're then told that if the total cost of the vacation had been divided equally among 4 PEOPLE, then the cost per person would have been $50 LESS. We're asked for the total cost of the vacation.

Looking at the answer choices, we can see that they're all 'nice' round numbers. Since the total cost was originally going to be divided among 3 people, that cost is almost certainly going to be a multiple of 3. Only answers B and E fit that pattern.

Let's TEST Answer B: $300

IF.... Total Cost = $300
Cost for 3 people = $100 each
Cost for 4 people = $75 each
Difference = $25
This is NOT a match for what we were told (the difference is supposed to be $50).
Eliminate Answer B.

Notice how $25 is exactly HALF of $50 though.... Maybe we need to DOUBLE all of the values....

Let's TEST Answer E: $600

IF.... Total Cost = $600
Cost for 3 people = $200 each
Cost for 4 people = $150 each
Difference = $50
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:
[Reveal] Spoiler:
E


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Re: The total cost of a vacation was divided among 3 people. If [#permalink]

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New post 12 Mar 2018, 18:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The total cost of a vacation was divided among 3 people. If   [#permalink] 12 Mar 2018, 18:23
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