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If 60 percent of the employees at company X are female, does company x have more than 100 female employees?

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by BTGModeratorVI » Thu Dec 03, 2020 2:58 pm

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If 60 percent of the employees at company X are female, does company x have more than 100 female employees?

(1) Company X has more than 150 employees
(2) Company X has 74 more female employees than male employees.

Answer: B
Source: official guide
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Re: If 60 percent of the employees at company X are female, does company x have more than 100 female employees?

by Brent@GMATPrepNow » Sun Dec 06, 2020 2:30 pm
BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:58 pm
 If 60 percent of the employees at company X are female, does company x have more than 100 female employees?

(1) Company X has more than 150 employees
(2) Company X has 74 more female employees than male employees.

Answer: B
Source: official guide
Given: 60 percent of the employees at company X are female
In other words: (number of female employees)/(TOTAL number of employees) = 60/100

Target question: Does company x have more than 100 female employees?

Statement 1: Company X has more than 150 employees
Let's test two cases that satisfy statement 1:
Case a: Company X has 1000 employees. So, the number of female employees = 60% of 1000 = 600. The answer to the target question is YES, the company has more than 100 female employees
Case b: Company X has 155 employees. So, the number of female employees = 60% of 155 = 93. The answer to the target question is NO, the company does not have more than 100 female employees
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Company X has 74 more female employees than male employees
Let M = number of male employees
So, M + 74 = number of female employees
So, the TOTAL number of employees = M + (M + 74) = 2M + 74

We already know that (number of female employees)/(TOTAL number of employees) = 60/100
Substitute values to get: (M + 74)/(2M + 74) = 60/100
ASIDE: Please note that, at this point, we need to only recognize that we COULD solve this equation for M, which means we COULD how to determine the total number of female employees.
So statement 2 must be sufficient, and we won't waste any time actually solving the equation.

Having said that, let's solve the equation for "fun"...
Simplify to get: (M + 74)/(2M + 74) = 3/5
Cross multiply to get: (3)(2M + 74) = (5)(M + 74)
Expand: 6M + 222 + 5M + 370
Solve: M = 148

So the number of female employees = M + 74 = 148 + 74 = 222
The answer to the target question is YES, the company has more than 100 female employees
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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