Data Sufficiency

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.

Viper83 wrote: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.

st 1)company has 151 emp
60% means somevalue less than 100 as we know 151/2 is 75 only
if company has 500 emp
60% means some value more than 100
dual case
A insufficient

2)we may think of supposing in this way 1 male emp and 74 females
but that will voilate 60% case,
when there is
F=M+74
ie M=F-74

Total=M+F

female/total x 100 =60
F/F-74+F x 100 =60
F/F-34 =6/5
5F=6F-204
F=204>100
so B


We can find value of Female which safies both condition
60% of total
female=74+1
only when female greater than 100 (ie 202)
so should be B
Otherwise both condition wont be met

My answer is B

First I simplified the prompt,as I almost always do.

Let the total no of employees =x

Then the question is "is 60/100 *x >100?"

or " x> 1000/6"

or " x> 166.67". The question is talking about integers so the rephrased question becomes " is x >= 167"

See I added equal to because it is allowable as per the equation "x>166.67"

So the real question is " Does the company have 167 or more employees?"

1) x>150.

X could be 160 or 170.

If 160 the answer to the question " Does the company have 167 or more employees?" is NO

If 170 then the answer is YES.

Hence INSUFFICIENT

2) If the number of males employees is m and the number of female employees is f,then f=m+74.

So the total no of employees = m+f = 2m+74.

60/100 (2m+74) = m+74
3/5(2m+74)=m+74
6m+222 = 5m+ 370
m= 148

So total no of employees = 2*148+74= 296+74=370

Since x=370

and we can say in a definitive way whether the no of employees in the company if 167 or more.

This statement is sufficient.

Hence B