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The total cost of a vacation was divided equally among 3

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by Jay@ManhattanReview » Mon Dec 02, 2019 9:30 pm
AAPL wrote: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

OA E
Say the cost of the vacation was $x; thus, share of each of the 3 people = x/3.

Had there been 4 people, the share of each of the 4 people had been = x/4.

Thus, x/3 - x/4 = 50

x = $600.

The correct answer: E

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Tue Dec 03, 2019 2:08 pm
AAPL wrote: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

OA 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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by [email protected] » Wed Dec 04, 2019 5:07 pm
Hi AAPL,

We're told that the total cost of a vacation was divided equally among 3 people and 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. This question can be solved in a couple of different ways, including 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. 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: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Thu Dec 05, 2019 7:02 pm
AAPL wrote: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

OA E
We let x = the total cost of the vacation and create the equation:

x/4 = x/3 - 50

Multiplying both sides of the equation by 12, we have:

3x = 4x - 600

600 = x

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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