M13-17

Question

In a sales department, the ratio of female employees to male employees was \(\frac{6}{7}\). After hiring 3 more men, this ratio changed to \(\frac{3}{4}\). How many employees are currently in the sales department?

A. 24
B. 36
C. 39
D. 42
E. 45

Show Answer

Official Answer

D

A. 24
B. 36
C. 39
D. 42
E. 45

Bunuel · Answer

Official Solution:

In a sales department, the ratio of female employees to male employees was \(\frac{6}{7}\). After hiring 3 more men, this ratio changed to \(\frac{3}{4}\). How many employees are currently in the sales department?

A. 24
B. 36
C. 39
D. 42
E. 45

Show Answer

Official Answer

D

A. 24
B. 36
C. 39
D. 42
E. 45

Initially, the ratio  \frac{F}{M} = \frac{6}{7} , and after hiring 3 more men, it became  \frac{F}{(M + 3)} = \frac{3}{4} . Solving this system of equations yields  F = 18  and  M = 21 . The total number of employees in the department now is  F + (M + 3) = 42 .

Answer: D

safaria25 · Answer

Hey Bunuel,

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

Thanks!

Bunuel · Answer

\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.

r19 · Answer

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

Bunuel · Answer

It should be 6x+7x+3=42.

cledgard · Answer

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)

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

theresiaschendz · Answer

I don’t quite agree with the solution. I believe the question wording to be a bit misleading. The last part "How many employees are CURRENTLY in the sales department?" could be understood as the number of employees BEFORE the 3 men were added. Hence why 39 could be perceived as a valid answer option.

Bunuel · Answer

Your interpretation is incorrect. The question explicitly asks for the number of employees currently in the sales department, which refers to the total after hiring the 3 additional men. The phrasing aligns with standard problem-solving conventions, where "currently" indicates the present total, not the number before the change.

Since the initial number of employees was 39, and 3 more men were added, the correct answer is 42. There’s no ambiguity in the wording.

Sufyanp · Answer

I like the solution - it’s helpful. Got the right answer but wording confused me a little bit. The way it's worded is like it's asking for the original number of employees.

Prateek_Sood · Answer

I like the solution - it’s helpful.

M13-17

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