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

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Jan 24, 2019 5:24 am

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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

Source: Beat The GMAT — Problem Solving | Thu Jan 24, 2019 5:24 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Jan 24, 2019 5:33 am

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

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

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 24, 2019 5:35 am

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

Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Jan 24, 2019 10:01 am

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

Contact Rich at [email protected]

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Feb 01, 2019 5:20 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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