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The total cost of a vacation was divided equally among 3 people. If the total cost of the vacation had been divided...

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by BTGmoderatorLU » Tue May 04, 2021 12:38 pm
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The total cost of a vacation was divided equally 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 of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600

The OA is E
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Re: The total cost of a vacation was divided equally among 3 people. If the total cost of the vacation had been divided.

by Brent@GMATPrepNow » Wed May 05, 2021 6:41 am
BTGmoderatorLU wrote: ↑
Tue May 04, 2021 12:38 pm
 Source: GMAT Prep

The total cost of a vacation was divided equally 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 of the vacation?

A. $200
B. $300
C. $400
D. $500
E. $600

The OA is E
Let T = total cost of vacation
So, T/3 = cost per person with THREE people
And T/4 = cost per person with FOUR people

If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less.
In other words (cost per person with FOUR people) = (cost per person with THREE people) - $50
We can write: T/4 = T/3 - 50

At this point, we can EITHER test the answer choices OR solve the equation.
Let's solve the equation.

Take: T/4 = T/3 - 50
12 is the LCM of 3 and 4, so multiply both sides by 12 to get: 3T = 4T - 600
Solve: T = 600

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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