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

It is currently 11 Nov 2019, 16:00

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

Shawna and Jia worked together to paint a house. Combined they worked

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

Hide Tags

Find Similar Topics 
Director
Director
User avatar
V
Joined: 24 Oct 2016
Posts: 558
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 18 Aug 2018, 03:45
2
21
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (03:09) correct 33% (02:52) wrong based on 207 sessions

HideShow timer Statistics

Shawna and Jia worked together to paint a house. Combined they worked for a total of y hours. Before the job started, Shawna paid t dollars to purchase paint and other supplies for the job. When the job was completed, Shawna was given a total of d dollars to pay for the work as well as reimburse her for the supplies. If Shawna worked for x more hours than Jia, how much money should Shawna give to Jia such that Shawna and Jia are each paid the same hourly rate for their work?

A) \(\frac{(d-t)(y-x)}{2y}\)

B) \(\frac{(d-t)}{y}\)

C) \(\frac{(d-x)}{y} - t\)

D) \(\frac{(dx - t)}{2}\)

E) \(\frac{(d-t)(y+x)}{2y}\)

_________________
Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified


If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
Director
Director
User avatar
V
Joined: 24 Oct 2016
Posts: 558
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 18 Aug 2018, 03:50
2
2
dabaobao wrote:
Shawna and Jia worked together to paint a house. Combined they worked for a total of y hours. Before the job started, Shawna paid t dollars to purchase paint and other supplies for the job. When the job was completed, Shawna was given a total of d dollars to pay for the work as well as reimburse her for the supplies. If Shawna worked for x more hours than Jia, how much money should Shawna give to Jia such that Shawna and Jia are each paid the same hourly rate for their work?

A) \(\frac{(d-t)(y-x)}{2y}\)

B) \(\frac{(d-t)}{y}\)

C) \(\frac{(d-x)}{y} - t\)

D) \(\frac{(dx - t)}{2}\)

E) \(\frac{(d-t)(y+x)}{2y}\)


Official Solution (Credit: Manhattan Prep)



Step 1: Glance Read Jot

This problem contains a lot of words that you need to turn into equations so this problem is about Algebraic Translations. Also, note that there are variables in the answer choices. Jot down the variables and what you are solving for.

d = total pay
t = cost of supplies
y = total hours
x = additional hours worked by Shawna

Money to Jia? → Equal hourly wage



Step 2: Reflect Organize

When there are variables in the answers, choosing Smart Numbers is often a good strategy. The other possibility is to work the translations. In this case, the algebra is likely to get messy given the number of variables, so smart numbers may be the better choice. Both strategies are provided below.



Step 3: Work

Smart Numbers



Start by picking numbers for the variables in the problem. Since you will have to divide the dollar amounts by hours to calculate hourly wages, make the dollar values multiples of 10 and set the total hours equal to 10 to keep the division easy.

d = total pay = $100
t = cost of supplies = $20
y = total hours = 10
x = additional hours worked by Shawna = 2

Now, calculate the target values: the amount of money Shawna should give Jia to make their hourly wages equal.

The amount of money for total wages is equal to the total pay minus the supply costs:
$100 – $20 = $80

The hourly wage is the amount for wages divided by the total hours worked:
$80/10 = $8

Calculate the number of hours Jia worked. The two women worked a total of 10 hours and Shawna worked 2 more hours than Jia. Therefore, Shawna worked 6 hours and Jia worked 4 hours.

If Jia worked 4 hours and the hourly wage is $8, then she is owed $32 ($8 × 4).

$32 is your target value; this is the value you will get when you plug your smart numbers for the other variables into the correct answer.

Test Choice (A).

(d − t)(y + x)/2y=(100 − 20)(10 − 2)/2(10)=(80)(8)/20=4(8)=32

If you are short on time, you may choose to stop once you find a match for your target. Otherwise, test the remaining answers to ensure that no other answer matches the target.

Test Choice (B).

(d − t)/y=(100 − 20)/10=8


Test Choice (C).

(d − x)/y−t=((100 − 2)/10)−20≈−10


Test choice (D).

(dx − t)/2=(100(2) − 20)/2=90


Test choice (E).

(d − t)(y + x)/2y=(100 − 20)(10 + 2)/(2(10))=(80)(12)/20=48



Only choice (A) matches the target value.



Algebra



The goal on this problem is to calculate how much money Jia should receive so that the two women earn the same hourly wage. Multiply the number of hours Jia worked times the hourly wage.

Jia’s Pay = Jia’s Hours Worked × Hourly Wage

Consider how to calculate those two things separately.

Jia’s Hours Worked
Two pieces of information are provided about the hours: The total hours worked were y and Shawna worked x more hours. Create equations for J, the hours Jia worked, and S, the hours Shawna worked.

J + S = y
J + x = S

Since the answers are in terms of x and y (not S), solve for J in terms of these two variables.

J + S = y Substitute in for S.
J + J + x = y Subtract x from both sides.
2J = y ­­ – x Divide both sides by 2.
J=(y − x)/2

Hourly Wage
To calculate the hourly wage, subtract the money that serves as reimbursement for the supplies from the total pay, then divide by the total number of hours worked by both women.

Hourly wage = (d − t)/y

Finally, multiply Jia’s hours by the hourly wage to get the total amount of money owed to Jia.

(y − x)/2×(d − t)/y=(y − x)(d − t)/(2y)



The correct answer is (A).
_________________
Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified


If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
Current Student
avatar
S
Joined: 15 Aug 2016
Posts: 184
Location: India
Concentration: Technology, Operations
GMAT 1: 690 Q49 V35
GPA: 3.84
WE: Operations (Consulting)
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 06:59
I almost cried while attempting this question. So many variables so many conditions. It took me five minutes on the test and I still ended up getting it wrong.
Can such kind of questions come in the exam?
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 12:02
Micky1005 wrote:
I almost cried while attempting this question. So many variables so many conditions. It took me five minutes on the test and I still ended up getting it wrong.
Can such kind of questions come in the exam?

Hi Micky1005 ,

In my opinion, the question is absolute GMAT-like... but the official solution is NOT!

Please follow my reasoning (in the post below) after reading the question stem carefully (more than once) for (say) approximately one minute.

I explain: the first reading must be fast - say 20 seconds - for the brain to know which "drawers to open". The second reading takes double-time, to start "the structure"!

Important: this is not time-wasting... it is time-investment!

(This advice follows the GMATH method.)

If you have any doubts, please feel free to ask me about it.

Regards and success in your studies!
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 12:08
dabaobao wrote:
Shawna and Jia worked EACH ONE ALONE to paint a house. Combined they worked for a total of y hours. Before the job started, Shawna paid t dollars to purchase paint and other supplies for the job. When the job was completed, Shawna was given a total of d dollars to pay for the work as well as reimburse her for the supplies. If Shawna worked for x more hours than Jia, how much money should Shawna give to Jia such that Shawna and Jia are each paid the same hourly rate for their work?

A) \(\frac{(d-t)(y-x)}{2y}\)

B) \(\frac{(d-t)}{y}\)

C) \(\frac{(d-x)}{y} - t\)

D) \(\frac{(dx - t)}{2}\)

E) \(\frac{(d-t)(y+x)}{2y}\)

\(?\,\,\,:\,\,\,{\text{Jia}}\,\,{\text{fair}}\,\,{\text{payment}}\,{\text{for}}\,\,{\text{her}}\,\,{\text{work}}\)

The careful reading suggested (in the post above) is enough to understand the following:

1. The $t paid by Shawna is reimbursed, therefore what is paid for the work is simply $ (d-t) and THIS is the amount that must be divided.

Conclusion: alternative choices (C) and (D) are not good candidates.

2. If we imagine y=3 (3h for Shawna and Jia to work, each one alone) and x=1 (so that Jia works 1h and Shawna works 2h), we are sure
$(d-t) must be divided in three equal parts, and Jia deserves one third of it.

Conclusion: when we explore the particular case x=1 and y=3 , our FOCUS, in this case the TARGET expression, is (d-t)/3 (in dollars).

Checking (A), (B) and (E), there is only one survivor (check that), hence this choice (A) is the correct choice!


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 213
Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 12:42
1
Total hours worked = y hours
Shawn worked "x" more than Jia. Therefore , Jia worked \(\frac{(y-x)}{2}\) hours

Shawn paid "t" for supplies. He received "d" as total payment + reimbursement for supplies.
Let k be their hourly rate which is same for both.

d = t + ky

=>\(\frac{(d-t)}{ky} = 1\) (wage for 1 hour)

=> \(\frac{(d-t)}{ky} * \frac{(y-x)k}{2}\) = Jia's wage

=> \(\frac{(d-t)(y-x)}{2y}\)
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 15:46
dabaobao wrote:
Shawna and Jia worked EACH ONE ALONE to paint a house. Combined they worked for a total of y hours. Before the job started, Shawna paid t dollars to purchase paint and other supplies for the job. When the job was completed, Shawna was given a total of d dollars to pay for the work as well as reimburse her for the supplies. If Shawna worked for x more hours than Jia, how much money should Shawna give to Jia such that Shawna and Jia are each paid the same hourly rate for their work?

Very nice approach, pandeyashwin !

Without exploring a particular case (as I did previously), let´s show the "GMATH´s way", using UNITS CONTROL, one of the most powerful tools of our method!

\(?\,\,\,\,:\,\,\,\,{\rm{Jia}}\,\,{\rm{fair}}\,\,\$ \,\,{\rm{payment}}\,{\rm{for}}\,\,{\rm{her}}\,\,{\rm{work}}\,\,\,\,\,\,\,\,\left[ {\,\$ \,c\,\,\, = \,\,\,{\rm{common}}\,\,{\rm{hourly}}\,\,\,{\rm{rate}}\,} \right]\,\,\,\)

\(y\,\,{\rm{h}}\,\,\,\left\{ \matrix{
\,{\rm{Shawna}}\,\,:\,\,\left( {{y \over 2} + {x \over 2}} \right)\,\,{\rm{h}} \hfill \cr
\,{\rm{Jia}}\,\,:\,\,\left( {{y \over 2} - {x \over 2}} \right)\,\,{\rm{h}} \hfill \cr} \right.\,\,\,\,\,\,\,\left[ {\,{\rm{Sum}}\,\,y\,\,,\,\,\,x\,\,{\rm{difference}}\,\,{\rm{,}}\,\,{\rm{Shawna}}\,\,{\rm{more}}\,\,{\rm{time}}\,} \right]\)

\(\left( {{{y + x} \over 2}} \right)\,\,{\rm{h}}\,\, \cdot \,\,\left( {{{\,\$ \,\,c\,} \over {1\,\,{\rm{h}}}}} \right)\,\,\,\,\, + \,\,\left( {{{y - x} \over 2}} \right)\,\,{\rm{h}}\,\, \cdot \,\,\left( {{{\,\$ \,\,c\,} \over {1\,\,{\rm{h}}}}} \right)\,\,\,\, = \,\,\,\,\$ \,\,\left( {d - t} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,yc = d - t\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,c = {{d - t} \over y}\,\,\,\,\,\left[ {\rm{$}} \right]\,\)

\(?\,\,\, = \,\,\,\,\left( {{{y - x} \over 2}} \right)\,\,h\,\,\, \cdot \,\,\,\left( {{{\,\$ \,\,\left( {d - t} \right)\,} \over {y\,\,\,{\rm{h}}}}} \right)\,\,\,\,\, = \,\,\,\,{{\,\left( {y - x} \right)\left( {d - t} \right)\,} \over {2y}}\,\,\,\,\,\,\left[ {\rm{\$ }} \right]\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Manager
avatar
P
Joined: 28 May 2018
Posts: 147
Location: India
Schools: ISB '21 (I)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 22 Oct 2018, 23:58
"Shawna and Jia worked together to paint a house. Combined they worked for a total of y hours".

If shawna and jia worked together, how come shawna worked for more number of hours than jia?

Why are we not using this:
s = time taken by shawna to do the work
j = time taken by jia to do the work

1/s + 1/j = 1/y ?

I understood the solution given by Manhattan, but if the question is worded in the above way, should we not follow this approach?
_________________
Please award KUDOS if my post helps. Thank you.
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 246
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 23 Oct 2018, 00:27
2
PriyankaPalit7 wrote:
"Shawna and Jia worked together to paint a house. Combined they worked for a total of y hours".

If shawna and jia worked together, how come shawna worked for more number of hours than jia?

Why are we not using this:
s = time taken by shawna to do the work
j = time taken by jia to do the work

1/s + 1/j = 1/y ?

I understood the solution given by Manhattan, but if the question is worded in the above way, should we not follow this approach?


PriyankaPalit7,

When we say " They worked together or simultaneously for y hours" => Shawna worked for y hrs and Jia also worked for y hrs.

On the other hand, if we say "Combined they worked for a total of y hours" => Shawna worked for a hrs (say) and Jia worked for b hrs (say), then a+b = y hrs.

i.e.
Combined they worked for a total of y hours \(\neq\) they worked together for y hours.

Hope this helps.

Thanks.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 23 Oct 2018, 05:51
Hi PriyankaPalit7 !

"Shawna and Jia worked together to paint a house." was something that bothered me, too.

Please have a look at my posts above, in which I changed (slightly) the question stem to avoid this confusion.

Regards and success in your studies!
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8338
Location: United States (CA)
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 23 Oct 2018, 19:21
dabaobao wrote:
Shawna and Jia worked together to paint a house. Combined they worked for a total of y hours. Before the job started, Shawna paid t dollars to purchase paint and other supplies for the job. When the job was completed, Shawna was given a total of d dollars to pay for the work as well as reimburse her for the supplies. If Shawna worked for x more hours than Jia, how much money should Shawna give to Jia such that Shawna and Jia are each paid the same hourly rate for their work?

A) \(\frac{(d-t)(y-x)}{2y}\)

B) \(\frac{(d-t)}{y}\)

C) \(\frac{(d-x)}{y} - t\)

D) \(\frac{(dx - t)}{2}\)

E) \(\frac{(d-t)(y+x)}{2y}\)


We are given that both Shawn and Jia worked for y hours. Since Shawna worked for x more hours than Jia, she worked (y + x)/2 hours and Jia worked (y - x)/2 hours. (Notice that (y + x)/2 + (y - x)/2 = 2y/2 = y and (y + x)/2 - (y - x)/2 = 2x/2 = x.)

Since Shawna paid t dollars for paint and supplies and was paid d dollars for the job and reimbursement, she received (d - t) dollars for the time she and Jia worked. Since they worked a total of y hours, the hourly wage should be
(d - t)/y dollars per hour. Since Jia worked (y - x)/2, then he should receive

(d - t)/y * (y - x)/2 = (d - t)(y - x)/(2y) dollars

Answer: A
_________________

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.

Manager
Manager
avatar
B
Joined: 07 Apr 2018
Posts: 101
Location: United States
Concentration: General Management, Marketing
GMAT 1: 600 Q45 V28
GPA: 3.8
Re: Shawna and Jia worked together to paint a house. Combined they worked  [#permalink]

Show Tags

New post 24 Oct 2018, 17:04
"Shawna was given a total of d dollars to pay for the work".. i messed up. i thought for Shawna's work :(
GMAT Club Bot
Re: Shawna and Jia worked together to paint a house. Combined they worked   [#permalink] 24 Oct 2018, 17:04
Display posts from previous: Sort by

Shawna and Jia worked together to paint a house. Combined they worked

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





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