Problem Solving

AAPL 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 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

Hi All,

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

To start, since the answers are all nice "round" numbers, it's likely that the total will be a multiple of 3 (since it will divide evenly among 3 people). That means the correct answer is likely either $300 or $600, since those are the only two answers that are evenly divisible by 3. Let's TEST Answer B first...

Answer B: $300
$300/3 = $100
$300/4 = $75
The difference is $100 - $75 = $25. This is TOO SMALL (notice that it's exactly HALF of what it needs to be though....), so we need the total to be GREATER.

Answer E: $600
$600/3 = $200
$600/4 = $150
The difference is $200 - $150 = $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

AAPL wrote:GMAT Prep

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 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