AAPL wrote: ↑Mon Apr 06, 2020 5:28 am
GMAT Prep
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.
OA
B
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
