Question: What is the number of female employees in Company X ?

(1) If Company X were to hire 14 more people and all of these people were females, the ratio of the number of male employees to the number of female employees would then be 16 to 9.
(2) Company X has 105 more male employees than female employees.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Solutions and Explanation

Approach Solution : 1

Statement - 1 : If Company X were to hire 14 more people and all of these people were females, the ratio of the number of male employees to the number of female employees would then be 16 to 9
This implies that,
X+14 = M+F+14
M/F+14 = 16/9
M9 = 16F + 224—--let this be equation 1
This is not sufficient as there are two unknowns and only one equation

Statement - 2 : Company X has 105 more male employees than female employees
M= F + 105 —-- let this be equation 2
X = F + F + 105
X = 2F + 105
This is not sufficient as there are two unknowns and only one equation
By analyzing both the statements, both equations are evaluated
We get,
9(F+105) = 16F + 224
9F + 945 = 16F + 224
721 = 7F
F = 103
Therefore, this is sufficient.

Correct Answer: (C)

“What is the number of female employees in Company X ?” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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