Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra : Problem Solving (PS)

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92760

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

16 Jan 2020, 01:49

Expert Reply

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

57% (01:36) correct

43% (01:48) wrong

based on 46 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

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

_________________

New to the GMAT CLUB Forum?

Ultimate GMAT Quantitative Megathread

All You Need for Quant

GMAT Club's Complete Questions' Bank

My Signature Questions' Collection:

Bunuel's Signature Questions' Collection

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Signature Read More

L

CareerGeek

VP

Joined: 20 Jul 2017

Posts: 1300

Location: India

Concentration: Entrepreneurship, Marketing

GMAT 1: 690 Q51 V30 Verified score

WE:Education (Education)

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

L

Leadership

Retired Moderator

Joined: 17 Dec 2018

Status:WHU MBA 2022 candidate

Posts: 932

Location: Germany

Concentration: Leadership, Operations

GMAT 1: 650 Q49 V29 Verified score

WE:Engineering (Manufacturing)

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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
_________________

JaSs

please send PM if you need advice

Signature Read More

L

Archit3110

GMAT Club Legend

Joined: 18 Aug 2017

Status:You learn more from failure than from success.

Posts: 8016

Location: India

Concentration: Sustainability, Marketing

GMAT Focus 1:
545 Q79 V79 DI73 Verified score

GPA: 4

WE:Marketing (Energy and Utilities)

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

L

Raxit85

Director

Joined: 22 Feb 2018

Posts: 754

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

D

Staphyk

Senior Manager

Joined: 20 Mar 2018

Posts: 476

Location: Ghana

Concentration: Finance, Statistics

GMAT 1: 710 Q49 V39

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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
_________________

Veritas valet et vincet

Signature Read More

D

exc4libur

SVP

Joined: 24 Nov 2016

Posts: 1720

Location: United States

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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)

L

freedom128

Director

Joined: 30 Sep 2017

Posts: 956

GMAT 1: 720 Q49 V40 Verified score

GPA: 3.8

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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.

D

eakabuah

Retired Moderator

Joined: 18 May 2019

Posts: 785

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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.

D

lacktutor

Director

Joined: 25 Jul 2018

Posts: 668

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

S

Jawad001

Manager

Joined: 14 Sep 2019

Posts: 223

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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)

S

neha283

Manager

Joined: 05 Oct 2017

Posts: 90

Location: India

Schools: Anderson '24 Fuqua '24 ISB '23 Johnson '24 Kellogg '24 Rotman '24

GMAT 1: 710 Q50 V35

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

D

QuantMadeEasy

Senior Manager

Joined: 28 Feb 2014

Posts: 471

Location: India

Concentration: General Management, International Business

GMAT 1: 570 Q49 V20 Verified score

GPA: 3.97

WE:Engineering (Education)

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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

L

KarishmaB

Tutor

Joined: 16 Oct 2010

Posts: 14815

Location: Pune, India

Re: Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra [#permalink]

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)

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

GMAT Problem Solving (PS) Questions

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

GMAT Question Banks