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

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


E

x/4=x/3-50 where x is total cost of vacation

x=600

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

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:

GMAT assassins aren't born, they're made,
Rich

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

\(? = 12T\,\,\,\,\left[ \$ \right]\)

\({\text{per}}\,\,{\text{person}}\,\,\,:\,\,\,\frac{{12T}}{3} = \frac{{12T}}{4} + 50\,\,\,\,\, \Rightarrow \,\,\,T = 50\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 600\,\,\,\,\left[ \$ \right]\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

\(\frac{x}{3} - \frac{x}{4} = 50\)

So, We know that x must be completely divisible by both 3 & 4

Least possible value of x is LCM of 3 & 4 = 12

Now, Check the options, Only (E) 600 is divisible by 12, thus Answer must be (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
_________________

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


E

This is really a question about averages, and whenever you see a question about averages on the GMAT - regardless of whether it seems like an easy one or a hard one - ALWAY ALWAYS ALWAYS write the average formula!!!

Here's an explanation of this question on YouTube:

https://www.youtube.com/watch?v=o1ZyM_M ... 6QYo5Jb-lY

The answer is (E)

total cost among 4 people= 4x (total amount)
total cost among 3 people= 3x+150

4x=3x+150
x=150
so, 4x= 600 (total amount)

Thanks!

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________