NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 14:05 It is currently 25 Apr 2024, 14:05
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619012 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 01:49
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

58% (01:43) correct 42% (01:48) wrong based on 47 sessions
Hide Show timer Statistics

Competition Mode Question



Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
ShowHide Answer
Official Answer
D
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3450 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 02:03
1
Kudos
For 40 hours, Salary = $20
—> Salary for 1 hour = \(\frac{ 20}{40} = $ 0.5 \)

salary per hour after 40 hours = 1/6 more tuan normal salary = 7/6th of 0.5 = \(\frac{ 7}{6 }*0.5 = $\frac{ 7}{12 } \)

Let the number of hours worked beyond 40 = \( x\)
—> Overtime salary earned = \( 23.5 - 20 = 3.5 \)
—> \(\frac{ 7}{12}* x = 3.5 \)
—> \( x = 3.5* \frac{ 12}{7 } = 6 \) hours

So, total hours worked = 40 + 6 = 46

Option D

Posted from my mobile device
User avatar
L
Leadership
Retired Moderator
Joined: 17 Dec 2018
Status:WHU MBA 2022 candidate
Posts: 932
Own Kudos [?]: 512 [1]
Given Kudos: 73
Location: Germany
Concentration: Leadership, Operations
GMAT 1: 650 Q49 V29
WE:Engineering (Manufacturing)
Send PM
Reviews Badge
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 02:32
1
Kudos
We know 40 hours = $20 ... overtime earned - $23.5 - $20 = $3.5
1 hour = $ \(\frac{20}{40}\) = $0.5

Overtime - Salary/hr after 40 hours = 1/6 times the normal salary - \(1 + \frac{1}{6} = \frac{7}{6}\)
We can writes as - \(\frac{7}{6} * 0.5\) = \(\frac{3.5}{6}\)

Let the number of hours worked after 40 hours as x and we already know that overtime earned is $3.5
\(\frac{3.5 * x}{6 } = 3.5\)
x=6

Total time - normal + overtime - 40 + 6 = 46

'D' is the winner
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8019
Own Kudos [?]: 4097 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 03:02
gross wage per 40 hour week = 20$ ; per hour earning ; 20/40 ; .5 $
and overtime ; .5*1/6 ; .083 ; $.583
so as to earn $23.5 ; i.e more than $3.5 than her usual time Blake would have to work ;
3.5/.583 ; ~ 6 hrs more
total hrs ; 46 hrs
IMO D


Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
User avatar
L
Raxit85
Director
Director
Joined: 22 Feb 2018
Posts: 754
Own Kudos [?]: 1022 [1]
Given Kudos: 134
Send PM
GMAT ToolKit User
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 03:14
1
Kudos
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47

$20/40 hrs = $ 0.5/hr. So, hourly rate is $0.5.
I don't know to proceed traditionally but ill try from the options.
Let me try with 46 hrs. If blake's total extra required hours = 6, then he earns $3 extra, but here condition also applies.
For 1 hr, 1/6*0.5 = 0.083, so for 6 hrs, 0.083*6 = 0.49 = 0.5.
So, 20 + 3 + 0.5 = 23.5.

Imo. D
User avatar
D
Staphyk
Senior Manager
Senior Manager
Joined: 20 Mar 2018
Posts: 476
Own Kudos [?]: 352 [0]
Given Kudos: 149
Location: Ghana
Concentration: Finance, Statistics
GMAT 1: 710 Q49 V39
Send PM
Reviews Badge
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 03:39
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.
Goal: ?hrs — wk ——- 23.50

Let hrs =hours , wk= week
Started:40hrs ——— wk——— $20
Overtime wage = 7/6(Gross wage) = $23.33
Let’s find #of hrs $23.33 overtime
Started: 2hrs———- wk——— $1
Accumu. : 46.66hrs——wk—$23.33

Since we started with
40hrs———-wk———-$20.00
Overtime: 6.66hrs—-wk——$3.33
Overtime: 1hr —-wk——$0.50
Goal : (47)1hr—-wk—— $0.50(47)
Goal : 47hrs—wk—$23.50

Hit that E ;)

Posted from my mobile device
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [1]
Given Kudos: 607
Location: United States
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 06:55
1
Kudos
Quote:
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47


total wage in week = $20 for 40 hours
normal wage per hour = $20/40 = $1/2
overtime wage per hour = $1/2*7/6 = $7/12

normal time $20 = 40 hours
overtime $3.5 = $3.5/7/12 = 6 hours
total time = 46 hours

Ans (D)
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   Updated on: 16 Jan 2020, 08:15
1
Kudos
Overtime rate = (7/6) * $20/40 =$7/12 per hour

Income = normal-hour + overtime
$23.5 = $20 + $(7/12)*h
h = 6 hours

Total hours per week= 40+h = 46 hours.
FINAL ANSWER IS (D)

Originally posted by freedom128 on 16 Jan 2020, 08:14.
Last edited by freedom128 on 16 Jan 2020, 08:15, edited 1 time in total.
User avatar
D
eakabuah
Retired Moderator
Joined: 18 May 2019
Posts: 785
Own Kudos [?]: 1040 [1]
Given Kudos: 101
Send PM
GMAT ToolKit User
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 08:14
1
Kudos
Per hour rate for 40hr week = 20/5 = 0.5
Per hour rate for overtime = 7/6 * 1/2 = 7/12

Jake received 23.5 for a week, hence his total pay for overtime in the week = 3.5 = 7/2
Number of extra hours put in by Jake = (7/2)/(7/12) = (7*12)/(2*7) = 6 hours

So Jake had to work for 46 hours in order to earn $43.5

The answer is D.
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1119 [1]
Given Kudos: 69
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 10:15
1
Kudos
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

Gross wage —$20 for a 40 hour week
—> hourly —$\(\frac{20}{40} = $0.5\)

Overtime —\((\frac{1}{2})+ (\frac{1}{6})*(\frac{1}{2})= \frac{1}{2}+ \frac{1}{12} =$ \frac{7}{12}\) (hourly)

—> 23.5 —20 = $3.5 (for overtime paid)
—> \(\frac{3.5}{(7/12)}=( \frac{7}{2})* (\frac{12}{7}) = 6\) hours

—> 40+ 6 = 46 hours (in total )

The answer is D

Posted from my mobile device
User avatar
S
Jawad001
Manager
Manager
Joined: 14 Sep 2019
Posts: 223
Own Kudos [?]: 138 [1]
Given Kudos: 31
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 12:33
1
Kudos
Given that, Time is 40 hours in a week
Gross wage = $20

Gross wage per hour = 20/40 =1/2
Over time per hour = ½*(7/6) = 7/12
Now,
20 + (x-40)*7/12 = 23.50
(x-40) * 7/12 = 3.5
x-40 = 3.5*(12/7)
x-40 = 6
x =46

Total number of hours = 46(D)
avatar
S
neha283
Manager
Manager
Joined: 05 Oct 2017
Posts: 90
Own Kudos [?]: 41 [1]
Given Kudos: 103
Location: India
Schools: Anderson '24 Fuqua '24 ISB '23 Johnson '24 Kellogg '24 Rotman '24
GMAT 1: 710 Q50 V35
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 18:28
1
Kudos
40 hr -->gross is 20$
1 hr -->gross is 0.5$
Blake has to earn 23.5$ this week, means 3.5$ in overtime.
overtime for 1 hour = 0.5 + 1/6*0.5 = 7/12
3.5 = 7/2
so, if he works for 6 hours overtime, 7/12 * 6 = 7/2 = 3.5$
so, D. 46 is the answer
User avatar
D
QuantMadeEasy
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 471
Own Kudos [?]: 559 [1]
Given Kudos: 74
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE:Engineering (Education)
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 20:02
1
Kudos
Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.
Hourly regular wage = $20/40 = $1/2
Hourly overtime wage = (7/6)(1/2) = 7/12
Total overtime eage = 3.50
Hence, (7/12)*x = 7/2
x = 6
Total number of hours = 40+6 = 46

D is correct
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64922 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink] New post   16 Jan 2020, 21:13
1
Kudos
Expert Reply
Normal wage per hour = 20/40 = $0.50
To make an extra $3.50, he would need to work 7 regular hours. But this money was made from overtime hours in which every hour pays 1/6th of the salary extra. So he needs to work only 6 hrs to make what he earns in 7 regular hrs.
Hence he will work 40 + 6 = 46 hrs

Answer (D)
GMAT Club Bot
gmatclubot
Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]
16 Jan 2020, 21:13
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions