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

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Intern
Joined: 27 Feb 2016
Posts: 2
In a certain company, the ratio of the number of managers to the [#permalink]

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25 Jul 2016, 17:10
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In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers:

a) 36
b) 37
c) 38
d) 39
e) 40

I need help because this question was discussed a lot in our group and some of us do not agree with the OA.

[Reveal] Spoiler: OA
SC Moderator
Joined: 13 Apr 2015
Posts: 1600
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)
Re: In a certain company, the ratio of the number of managers to the [#permalink]

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25 Jul 2016, 20:20
M/NM > 5x/24x

M = 8
8/NM > 5x/24x
8/NM - 5x/24x > 0
(192x - 5x * NM)/(24x * NM) > 0
192x - 5x*NM > 0
5x*NM < 192x
NM < 192x/5x
NM < 38.4
Maximum number of non managers = 38

Math Expert
Joined: 02 Sep 2009
Posts: 44288
Re: In a certain company, the ratio of the number of managers to the [#permalink]

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25 Jul 2016, 23:29
eduardofp wrote:

In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers:

a) 36
b) 37
c) 38
d) 39
e) 40

I need help because this question was discussed a lot in our group and some of us do not agree with the OA.

This is a copy of the following GMAT Prep question: at-a-certain-university-the-ratio-of-the-number-of-teaching-103543.html

Hope it helps.
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VP
Joined: 22 May 2016
Posts: 1416
In a certain company, the ratio of the number of managers to the [#permalink]

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29 Aug 2017, 13:53
eduardofp wrote:

In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers:

a) 36
b) 37
c) 38
d) 39
e) 40

Let M = managers
Let x = non-managers

"[T]he ratio of the number of managers to the number of non-managers [] must always be greater than 5 : 24" -->

$$\frac{M}{x} > \frac{5}{24}$$

Maximum number of non-managers if there are 8 managers?

$$\frac{8}{x} > \frac{5}{24}$$

Cross multiply (the numbers are positive):

$$(24)(8) > 5x$$

$$192 > 5x$$

$$38.4 > x$$, or $$x < 38.4$$

The number of non-managers must be fewer than 38.4 -- AND we want the maximum possible number of non-managers. We need the integer just below 38.4, which is 38.

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At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116
Re: In a certain company, the ratio of the number of managers to the [#permalink]

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05 Sep 2017, 18:21
eduardofp wrote:

In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers:

a) 36
b) 37
c) 38
d) 39
e) 40

We can create the following inequality:

8/n > 5/24

192 > 5n

38.4 > n

So, the maximum number of non-managers is 38.

_________________

Jeffery Miller

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Re: In a certain company, the ratio of the number of managers to the   [#permalink] 05 Sep 2017, 18:21
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