In a certain company, the ratio of the number of manager to

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

In a certain company, the ratio of the number of manager to

by swerve » Tue Oct 23, 2018 11:57 am

Timer

00:00

Your Answer

Global Stats

In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

The OA is D.

Source: Official Guide

Quote

Source: Beat The GMAT — Problem Solving | Tue Oct 23, 2018 11:57 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Oct 23, 2018 12:26 pm

swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

The OA is D.

Source: Official Guide

One option is to use TWO VARIABLES

Let M = CURRENT # of managers
Let W = CURRENT # of production-line workers

The ratio of the number of managers to the number of production-line workers is 5 to 72.
So, we can write: M/W = 5/72
Cross multiply to get: 5W = 72M

If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74
If 8 workers are hired then:
W + 8 = NEW number of workers
Also, M = number of managers (since nothing changes with the managers).
We can now write: M/(W + 8) = 5/74
Cross multiply to get: 74M = 5(W + 8)
Expand: 74M = 5W + 40
Rearrange to get: 74M - 40 = 5W

So, we now have two equations: 5W = 72M and 74M - 40 = 5W

Since BOTH equations are set equal to 5W, we can conclude that 72M = 74M - 40
Subtract 74M from both sides to get: -2M = -40
Solve to get M = 20

So, there are 20 managers.

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Tue Oct 23, 2018 2:37 pm

swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

Source: Official Guide

Excellent opportunity for the k technique:
$$\left\{ \matrix{
\,{\rm{managers}} = 5k \hfill \cr
\,{\rm{workers}}\, = \,\,72k \hfill \cr} \right.\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,? = 5k$$
$${{5k} \over {72k + 8}} = {5 \over {74}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{and}}\,\,{\rm{cross - multiply}}}^{:\,\,5} \,\,\,\,\,\,74k = 72k + 8\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k = 4\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 20$$

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Quote

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Tue Oct 23, 2018 2:43 pm

Hi swerve,

We're told that the ratio of the number of manager to the number of production-line workers is 5 to 72 - and IF 8 additional production-line workers were to be hired, then the ratio of the number of managers to the number of production-line workers would be 5 to 74. We're asked for the number of managers that the company has. This question can be approached in a number of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first:

Answer B: 10 manages

Since we have a ratio of 5 managers to 72 workers, we would have
10 managers & 144 workers
After adding 8 more workers, we would have...
10 managers & 152 workers
This ratios is...5:76, which is NOT a match for what we're looking for (we want 5:74, so we'll need more managers)

Answer D: 20 managers

Since we have a ratio of 5 managers to 72 workers, we would have
20 managers & 288 workers
After adding 8 more workers, we would have...
20 managers & 296 workers
This ratio is 5:74, which is a MATCH for what we're looking for, so this must be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Oct 25, 2018 8:22 am

swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

We are given that the ratio of managers to production-line workers is 5 to 72, or 5x to 72x. We can create the following equation:

(5x)/(72x + 8) = 5/74

74(5x) = (72x + 8)(5)

370x = 360x + 40

10x = 40

x = 4

The company has 4*5 = 20 managers.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]