Data Sufficiency

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.

The answer is C, but how do you set up the equations to solve the problem?

Let the number of males be M & number of females be F
1. upon adding 16 females the ratio is: M : (F+16) = 16:9 Not sufficient (need the current ratio also for solving)
2. M - F = 105 (not sufficient, need one more eqation between M & F)

Now put these two together: SUFFICIENT: C is the answer


Let me know in case of any doubts.

Regards,
Bharat.

Bharat,

Just a small correction, tere is a typo. It should be 14 of new employees not 16.

Thanks for the correction.
Have a beautiful day ahead.

Regards,
Bharat.

jaydeer44 wrote: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.

The answer is C, but how do you set up the equations to solve the problem?

Here's the great thing about data sufficiency: you don't NEED to set up the equations to answer the question, you just need to recognize what kind of equations you have.

(1) we can turn this into one equation with 2 variables, F and M. One equation, two unknowns: no way to solve, insufficient.

(2) we can turn this into one equation with 2 variables, F and M. One equation, two unknowns: no way to solve, insufficient.

Combined: we have two distinct linear equations and 2 unknowns: we can solve for everything, sufficient!

The "number of equations vs number of unknowns" rule is THE most powerful tool in data sufficiency. The better you know the rule (and the common exceptions), the more quickly you'll be able to burn through DS questions without actually doing the math (which should be your goal, since you don't get any bonus points for actually getting the answer).

Stuart, thanks a lot for reminding to stay focussed.

Regards,
Bharat.