What is the number of female employees in

[avinash.sunnasy]

(DS Problem)

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.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH Statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

:------------------------------------------------------:

Hello all,

I can solve this problem, however it takes me a long time, almost 4 minutes.

There must be something I'm missing?

STEP 1:-

Simplify the question.

X = M + F

what is F?

STEP 2:-

Analyse statement (1)

X+14 = M+F+14

M/F+14 = 16/9

(EQ1) M9 = 16F + 224

Insufficient

STEP 3:-

Analyse statement (2)

(EQ2) M= F + 105

X = F + F + 105

X = 2F + 105

Insufficient

STEP 4:-

Analyse statement (1) & (2)

Substitute (EQ2) into (EQ1)

9(F+105) = 16F + 224

(At this point, I know the answer is (C), and perhaps this is where I've lost time, since I continue to solve)

9F + 945 = 16F + 224
721 = 7F

F = 103

Sufficient

[gokul_nair1984]

Dude....Never solve DS questions...All you have to do is check for data sufficiency.

Stem :

Let no. of male employees=M=x
Let no. of female employees=F=y
Total=x+y

To Find y=?

Case 1:
M=x
F=y+14
x/(y+14)=16/9
Can we find the value of y? No because there is only 1 equation and 2 unknowns.

Case 2:

M-F=x-y=105
Again not possible to find the value of y as there is only 1 equation and 2 unknowns.


Combining the two statements we have,
x/(y+14)=16/9...(1)
x-y=105............(2)

There has to be a uniques solution as we now have two different equations and 2 unknowns. Thus the answer is C.
Do not solve as it will be time consuming. Your final solution is correct by the way.


PS: Do analyze the 2 equations just to make sure they are not the same as it would then yeild infinite number of solutions.

ex x+2y=5
2x+4y=10......These 2 equations are the same ...Beware of such traps

[RonPurewal]

the key to solving this problem is to recognize how to write the equations according to what's given. remember that, as this is a DS problem, there is no need to solve the equations -- you only need to determine WHETHER you can solve them.

(DS Problem)

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.

there's no relationship between the numbers of male and female employees, so use two variables, M and F.
this statement can be written
M / (F + 16) = 16/9
this is insufficient; there are lots and lots of values of M and F that will solve it.
if you want, you can multiply it out, to give 9M = 16F + 256. this is unnecessary at this point, but it reveals that you're dealing with a linear equation (an important fact when it comes to combining equations in the future).

(2) Company X has 105 more male employees than female employees.

--> M = F + 105
insufficient by itself.

TOGETHER:
there are two *independent* linear equations (i.e., they are not just multiples of each other, which would lead to a situation in which they'd still be insufficient if taken together).
therefore, they can be solved together.

answer should be (c).

to the original poster -- what took you 4 minutes here? the above equations require a fair amount of reading, but they are not especially complicated; if you took that much time to interpret them and convert them into mathematical equations, you may want to check out a high school algebra book for more practice on word problems so that you can get your speed up.