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# M13-17

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Math Expert
Joined: 02 Sep 2009
Posts: 45213

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16 Sep 2014, 00:49
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Question Stats:

78% (01:29) correct 22% (01:01) wrong based on 100 sessions

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In a sales department the ratio of female employees to male employees was $$\frac{6}{7}$$. If after 3 more men were hired, this ratio dropped to $$\frac{3}{4}$$, how many employees are there in the sales department now?

A. 21
B. 24
C. 36
D. 42
E. 45
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:49
Official Solution:

In a sales department the ratio of female employees to male employees was $$\frac{6}{7}$$. If after 3 more men were hired, this ratio dropped to $$\frac{3}{4}$$, how many employees are there in the sales department now?

A. 21
B. 24
C. 36
D. 42
E. 45

It was $$\frac{F}{M} = \frac{6}{7}$$ and it became $$\frac{F}{(M + 3)} = \frac{3}{4}$$. This system of equations gives $$F = 18$$ and $$M = 21$$. The total number of employees in the department now is $$M + F + 3 = 42$$.

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22 Sep 2014, 20:14
Bunuel wrote:
Official Solution:

In a sales department the ratio of female employees to male employees was $$\frac{6}{7}$$. If after 3 more men were hired, this ratio dropped to $$\frac{3}{4}$$, how many employees are there in the sales department now?

A. 21
B. 24
C. 36
D. 42
E. 45

It was $$\frac{F}{M} = \frac{6}{7}$$ and it became $$\frac{F}{(M + 3)} = \frac{3}{4}$$. This system of equations gives $$F = 18$$ and $$M = 21$$. The total number of employees in the department now is $$M + F + 3 = 42$$.

Hey Bunuel,

From the system of equations, can you please illustrate how you got F=18 and M=21?

Thanks!
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Joined: 02 Sep 2009
Posts: 45213

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23 Sep 2014, 00:52
safaria25 wrote:
Bunuel wrote:
Official Solution:

In a sales department the ratio of female employees to male employees was $$\frac{6}{7}$$. If after 3 more men were hired, this ratio dropped to $$\frac{3}{4}$$, how many employees are there in the sales department now?

A. 21
B. 24
C. 36
D. 42
E. 45

It was $$\frac{F}{M} = \frac{6}{7}$$ and it became $$\frac{F}{(M + 3)} = \frac{3}{4}$$. This system of equations gives $$F = 18$$ and $$M = 21$$. The total number of employees in the department now is $$M + F + 3 = 42$$.

Hey Bunuel,

From the system of equations, can you please illustrate how you got F=18 and M=21?

Thanks!

$$\frac{F}{M} = \frac{6}{7}$$ --> 7F = 6M;

$$\frac{F}{(M + 3)} = \frac{3}{4}$$ --> 4F = 3M + 9 --> multiply by 2, so that coefficients of M in both equations to be the same: 8F = 6M + 18.

Subtract first equation from second: F = 18. Substitute in first equation: 7*18 = 6M --> M = 7*3 = 21.

Hope it's clear.
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17 Aug 2016, 10:01
why my logic is wrong can someone explain me please?

equation 6x/(7x+3)= 3/4
on solving this we get x=3

therefore number of employees now are 3*3 +4*4=21
Math Expert
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17 Aug 2016, 11:49
r19 wrote:
why my logic is wrong can someone explain me please?

equation 6x/(7x+3)= 3/4
on solving this we get x=3

therefore number of employees now are 3*3 +4*4=21

It should be 6x+7x+3=42.
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11 Oct 2016, 06:07
2
KUDOS
Thank god there was no 39 in the answer choices :D
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11 Oct 2016, 08:10
1
KUDOS
Bunuel wrote:
In a sales department the ratio of female employees to male employees was $$\frac{6}{7}$$. If after 3 more men were hired, this ratio dropped to $$\frac{3}{4}$$, how many employees are there in the sales department now?

A. 21
B. 24
C. 36
D. 42
E. 45

It can be solved by elimination.

After adding 3 M, there are 3 F for every 4 M; then the total must be a multiple of 7(3x + 4x = 7x), so the answer is either A or D.

Before adding 3 M, the ratio was 6 F to 7 M, so the total had to be a multiple of 13.

Then the answer is D: 39 (multiple of 13) + 3 = 42(multiple of 7)
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09 Feb 2018, 02:23
My non-algebraic but quick solution, using a ratio table:

Female : Male : Total
6 : 7 : 13

After quickly glancing at the answers, the highest number is 45, so we're only dealing with low multiples. Write out the first three sets:

F : M : T
6 : 7 : 13
12 : 14 : 26 (2x)
18 : 21 : 39 (3x)

When we add 3 more employees (gender doesn't matter), we will have 16, 29 or 42 employees. Of these, only 42 is one of the answer choices, so pick that.

A quick confirmation (not necessary):

F : M : T
18 : 24 : 42

It's easy to see at a glance that 18:24 = 3:4 which is the correct ratio.
Re: M13-17   [#permalink] 09 Feb 2018, 02:23
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# M13-17

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