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

Question

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

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

GMATBLACKBELT · Answer

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

E

pmenon · Answer

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

x=600

Nadiuska · Answer

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

EMPOWERgmatRichC · Answer

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:  E

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

BrentGMATPrepNow · Answer

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

fskilnik · Answer

? = 12T\,\,\,\,\left

{	ext{per}}\,\,{	ext{person}}\,\,\,:\,\,\,\frac{{12T}}{3} = \frac{{12T}}{4} + 50\,\,\,\,\, \Rightarrow \,\,\,T = 50\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 600\,\,\,\,\left

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

Regards, 
Fabio.

Abhishek009 · Answer

\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)

ScottTargetTestPrep · Answer

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

mbaprep2020 · Answer

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

E

RobertVericPrep · Answer

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)

ShailendraSYadav · Answer

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!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia