60% of the employees of Due North Inc. are female, and 75% of the men

Question

60% of the employees of Due North Inc. are female, and 75% of the men earn more than $25,000 per year. If 45% of the company’s employees earn more than $25,000 per year, what fraction of the women employed by the company earn $25,000 per year or less?

A. 2/11
B. 1/4
C. 1/3
D. 1/2
E. 3/4

Show Answer

Official Answer

E

A. 2/11
B. 1/4
C. 1/3
D. 1/2
E. 3/4

akadiyan · Answer

Lets assume total number of employees = 100
Female employees = 60% = 60
We now know that Male = 40% = 40

75% of the men earn more than $25,000 per year = 75% 0f 40 = 30 Employees
Now we know that 25% of men earn less than or equal to $25000 = 25% of 40 = 10 Employees

45% of the company’s employees earn more than $25,000 per year = 45% of 100 = 45 Employees

We can calculate % of female employees who earn more than $25000 per year = 45 - 30 = 15 Employees

% of female who earns <= $25000 = Total number of female employees - Number of employees earning >= $25000
 = 60 - 15 = 45

fraction of the women employed by the company earn $25,000 per year or less =  \frac{45}{60} =  \frac{3}{4}

Ans  E

twobagels · Answer

I picked 100 as a number to set percentages to integers for easy calculation.

gender | earning 25k +
Females | 60 | 15
Males | 40 | 30

Info was 75% of males earn over 25k, so I plugged in 30 for that and solved for the percent of females earning over 25k by using a weighted average formula as below

(x + 30)/100 = .45

so, percent of females earning less than 25k would be 60 - 15 = 45. 
answer 3/4, E

MathRevolution · Answer

Let the total employees be 1000

60% of the employees of Due North Inc. are female:  \frac{60 }{ 100} * 1000 = 600

Men employee: 1000 - 600 = 400

75% of men earn more than $25,000 per year: 75/100 * 400 = 300 men earn > $25,000.

45% of the company’s employees earn more than $25,000 per year:  \frac{45}{100} * 1000 = 450

A female employee earning more than $25,000: 450 - 300 = 150

Therefore, female earning $25,000 or less: 600 - 150 = 450

The fraction of the women employed by the company earned $25,000 per year or less:  \frac{450 }{ 600} = \frac{3}{4} .

Answer E

luisdicampo · Answer

Deconstructing the Question

60% of employees are  women , so 40% are  men . 
75% of  men  earn more than 25,000, so 25% of  men  earn 25,000 or less. 
45% of  all employees  earn more than 25,000, so 55% earn 25,000 or less. 
We need the fraction of  women  who earn 25,000 per year or less.

Step-by-step

Assume there are  100 employees . 
Then there are  60 women  and  40 men .

Men earning more than 25,000: 
 0.75 	imes 40 = 30

So men earning 25,000 or less: 
 40 - 30 = 10

Total employees earning more than 25,000: 
 0.45 	imes 100 = 45

So women earning more than 25,000: 
 45 - 30 = 15

Thus women earning 25,000 or less: 
 60 - 15 = 45

Required fraction: 
 \frac{45}{60} = \frac{3}{4}

Answer: 3/4

60% of the employees of Due North Inc. are female, and 75% of the men

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60% of the employees of Due North Inc. are female, and 75% of the men

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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