Machine A can produce toys at a constant rate of 2 units per hour and : Problem Solving (PS)

GMATinsight

GMAT Club Legend

Joined: 08 Jul 2010

Last visit: 13 Dec 2024

Posts: 6,071

Own Kudos:

14,602

Given Kudos: 125

Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator

Location: India

GMAT: QUANT+DI EXPERT

Schools: IIM (A) ISB '24

GMAT 1: 750 Q51 V41 Verified score

WE:Education (Education)

Products:

Expert reply

Schools: IIM (A) ISB '24

GMAT 1: 750 Q51 V41 Verified score

Posts: 6,071

Kudos: 14,602

22 Feb 2017, 02:06

Kudos

Bookmarks

AustinKL

GMATinsight

AustinKL

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E

Dear GMATinsight, Could you share with me why shall we consider the remaining job?

Because we need to ensure that work is done in 20 Hours which is a mentioned fact which needs to be abide by

BillyZ

Current Student

Joined: 14 Nov 2016

Last visit: 20 Oct 2024

Posts: 1,158

Own Kudos:

21,370

Given Kudos: 926

Location: Malaysia

Concentration: General Management, Strategy

Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)

GMAT 1: 750 Q51 V40 (Online) Verified score

GPA: 3.53

Products:

Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)

GMAT 1: 750 Q51 V40 (Online) Verified score

Posts: 1,158

Kudos: 21,370

22 Feb 2017, 06:03

Kudos

Bookmarks

Quote:

Because we need to ensure that work is done in 20 Hours which is a mentioned fact which needs to be abide by

Dear GMATinsight, However, the question is asking about greatest possible hours so that machine A & B can produce 88 units and not the remaining.

ganand

Joined: 17 May 2015

Last visit: 19 Mar 2022

Posts: 198

Own Kudos:

3,318

[]

Given Kudos: 85

Posts: 198

Kudos: 3,318

[]

22 Feb 2017, 07:32

2

Kudos

1

Bookmarks

AustinKL

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

Hi,
This problem can be thought as a three machine problem. Let's call A+B together as Machine C.
Let
Machine A works for \(x\) hrs @ 2unit/hr
Machine B works for \(y\) hrs @ 5 units/hr, and
Machine C works for \(z\) hrs @ 7 units/hr

Equation for time constraint:
\(x + y + z = 20\) --- (1)

Production constraint:
\(2x + 5y + 7z = 88\) --- (2)

Eqn(2) - 2*Eqn(1)
\(2x + 5y + 3z - 2x -2y -2z = 88 - 40 \Rightarrow 3y + 5z = 48 \Rightarrow z = \frac{48 - 3y}{5}\)

Maximum possible integral value of \(z = 9\) for \(y = 1\)

Answer: 9hrs (E).

Plug in the value of z and y in Eqn (1), we get x = 11. These values satisfy both the equations.

Thanks.

gracie

Joined: 07 Dec 2014

Last visit: 11 Oct 2020

Posts: 1,048

Own Kudos:

1,715

Given Kudos: 27

Posts: 1,048

Kudos: 1,715

22 Feb 2017, 11:45

Kudos

Bookmarks

AustinKL

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

quick and dirty approach:
let x=number of units produced by A and B
x/7+(88-x)/2=20 hrs
x≈67 units
67/7≈9 hrs
9
E

BillyZ

Current Student

Joined: 14 Nov 2016

Last visit: 20 Oct 2024

Posts: 1,158

Own Kudos:

21,370

Given Kudos: 926

Location: Malaysia

Concentration: General Management, Strategy

Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)

GMAT 1: 750 Q51 V40 (Online) Verified score

GPA: 3.53

Products:

Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)

GMAT 1: 750 Q51 V40 (Online) Verified score

Posts: 1,158

Kudos: 21,370

02 May 2017, 22:12

Kudos

Bookmarks

ziyuen

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

OFFICIAL EXPLANATION

If machine A produces toys for "a" hours and machine B produces toys for "b" hours, and both machine A and B produce toys for "c" hours at the same time, you get \(a+b+c=20\) ---(1).

\(2a+5b+(2+5)c=88\)
\(2a+5b+7c=88\) ---(2)

Multiply (1) by 2, \(2a+2b+2c=40\) ---(3).

Equation (2) minus Equation (3), \(3b+5c=48\) ---(4)

(a, b, c) = (10, 1, 9), (8, 6, 6), (6, 11, 3)

Among these, the possible maximum value of c is 9.

Answer : E

ishaan.wares

Joined: 14 May 2015

Last visit: 25 Mar 2018

Posts: 29

Own Kudos:

20

Given Kudos: 2

Posts: 29

Kudos: 20

05 May 2017, 09:41

Kudos

Bookmarks

a=2
b=5
a+b=7
option checking from higher value
option E
7*9=63
remain=88-63=25
2*10+5*1=25
answer:E

ShashankDave

Joined: 03 Apr 2013

Last visit: 26 Jan 2020

Posts: 221

Own Kudos:

263

[]

Given Kudos: 872

Location: India

Concentration: Marketing, Finance

Schools: McDonough '21 (A) Kelley '21 ISB '21 (I)

GMAT 1: 740 Q50 V41 Verified score

GPA: 3

Schools: McDonough '21 (A) Kelley '21 ISB '21 (I)

GMAT 1: 740 Q50 V41 Verified score

Posts: 221

Kudos: 263

[]

06 May 2017, 04:04

1

Kudos

Bookmarks

GMATinsight

AustinKL

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E

Good question, bad wording. Agree?

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 12 Dec 2024

Posts: 97,852

Own Kudos:

685,456

[]

Given Kudos: 88,266

Products:

Expert reply

Posts: 97,852

Kudos: 685,456

[]

31 May 2017, 10:36

1

Kudos

Bookmarks

hazelnut

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

Similar question to practice: https://gmatclub.com/forum/machine-a-pr ... 98123.html

premsmit

Joined: 08 Jul 2016

Last visit: 06 Mar 2020

Posts: 2

Own Kudos:

3

Given Kudos: 5

Posts: 2

Kudos: 3

05 Mar 2020, 23:29

Kudos

Bookmarks

Should not the question be like--

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work simaltaneously (insted of "together") at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

Sejal16

Joined: 20 Dec 2019

Last visit: 23 Dec 2020

Posts: 58

Own Kudos:

32

Given Kudos: 64

Location: India

Schools: ISB'22 (I)

GMAT 1: 730 Q50 V38 Verified score

Schools: ISB'22 (I)

GMAT 1: 730 Q50 V38 Verified score

Posts: 58

Kudos: 32

11 Mar 2020, 09:02

Kudos

Bookmarks

I am unsure of all the above solutions - question wants to maximize total hours of A&B such that they produce 88 units. Why not 88/7 = ~12 ? Why do we need to utilize all 20 hours ?

I initially interpreted the question in another manner - total machine hours should not exceed 20.

Please explain. This question appears super wierd

Kinshook

GMAT Club Legend

Joined: 03 Jun 2019

Last visit: 12 Dec 2024

Posts: 5,423

Own Kudos:

4,598

Given Kudos: 161

Location: India

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,423

Kudos: 4,598

11 Mar 2020, 09:25

Kudos

Bookmarks

hazelnut

Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs

Given: Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour.

Asked: If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

Let us assume that machine A and machine B work together at their constant rates for 9 hours

Toys produced in 9 hours = 7*9 = 63 toys

Remaining toys = 88 - 63 = 25 toys

If Machine A is used for 10 hours and Machine B for 1 hours, toys produced in 11 hours = 5 + 20 = 25 toys

IMO E

bumpbot

Non-Human User

Joined: 09 Sep 2013

Last visit: 04 Jan 2021

Posts: 35,806

Own Kudos:

929

Posts: 35,806

Kudos: 929

03 Mar 2022, 14:15

Kudos

Bookmarks

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Machine A can produce toys at a constant rate of 2 units per hour and

Prep Toolkit

My Rewards

GMAT Problem Solving (PS) Questions

Machine A can produce toys at a constant rate of 2 units per hour and

Prep Toolkit

My Rewards