GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 10 Dec 2019, 14:54

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The sum of the wages earned by Rachel, Robin and Richard in a week is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59634
The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

Show Tags

New post 19 Aug 2015, 01:11
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:31) correct 37% (03:40) wrong based on 54 sessions

HideShow timer Statistics

The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. It is also known that 4 times Rachel's wage is equal to 6 times Robin's wage and 8 times Richard's wage. How much is Rachel's wage more than that of Robin?

A. $300
B. $400
C. $600
D. $800
E. $1200



Kudos for a correct solution.

_________________
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

Show Tags

New post 19 Aug 2015, 03:56
Bunuel wrote:
The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. It is also known that 4 times Rachel's wage is equal to 6 times Robin's wage and 8 times Richard's wage. How much is Rachel's wage more than that of Robin?

A. $300
B. $400
C. $600
D. $800
E. $1200



Kudos for a correct solution.



Rachel=\(R_1\)
Robin=\(R_2\)
Richard = \(R_3\)
Let T = total of the above 3.

Given, \(4*R_1 = 6*R_2=8*R_3\) ----> T/4 + T/6+T/8 = 2600 --->13T/24=2600---> T=4800

Thus, \(R_1\) - \(R_2\) = T/4-T/6 = 1200-800 = 400. B is the correct answer.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15692
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

Show Tags

New post 04 Jan 2018, 16:17
Hi All,

One of the quirky aspects to this question is that all 3 names start with an "R" (which is is something the GMAT writers would rarely do). As such, I'm going to create 3 new variables to represent the wages that each person earned:

A = Rachel's wage
B = Robin's wage
C = Richard' wage

With the given information, we can create the following two equations:
A + B + C = 2600
4A = 6B = 8C

The second equation can be converted into a ratio; since we know that 4A = 6B = 8C, we can TEST VALUES and define the relationship among the three variables:

The 3 variables in this equation could be:
C=3, B=4 and A=6

Thus, we know that the ratio of A:B:C = 6:4:3... meaning that for every 3 dollars Richard earns, Robin earns 4 dollars and Rachel earns 6 dollars. Thus, the TOTAL wages must be a multiple of 13.... which they are ($2600). By extension, the ratio tells us that...
Rachel earned $1200
Robin earned $800
Richard earned $600

Thus Rachel earned $400 more than Robin.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8659
Location: United States (CA)
Re: The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

Show Tags

New post 20 Oct 2019, 10:01
Bunuel wrote:
The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. It is also known that 4 times Rachel's wage is equal to 6 times Robin's wage and 8 times Richard's wage. How much is Rachel's wage more than that of Robin?

A. $300
B. $400
C. $600
D. $800
E. $1200



Kudos for a correct solution.


We can create the equations:

R + B + D = 2600

and

4R = 6B

2R = 3B

2R/3 = B

and

4R = 8D

R/2 = D

Substituting into the first equation, we have:

R + 2R/3 + R/2 = 2600

Multiplying by 6, we have:

6R + 4R + 3R = 15,600

13R = 15,600

R = 1,200

So B = 800 and R - B = 1200 - 800 = 400.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: The sum of the wages earned by Rachel, Robin and Richard in a week is   [#permalink] 20 Oct 2019, 10:01
Display posts from previous: Sort by

The sum of the wages earned by Rachel, Robin and Richard in a week is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne