In an office that employs 120 people, m% of the employees are male, an

Question

In an office that employs 120 people, m% of the employees are male, and c% of the employees are members of the custodial staff. How many employees are females who are not members of the custodial staff?

(1) m + c = 50
(2) The number of female employees who are members of the custodial staff is four.

ShoeBunny · Answer

I'm thinking the answer may be C?

(1) m+c is 50 (I interpret this as 50% right?) so men and also custodians make up 60 employees. So remaining 60 must all women. But I don't know how many of those 60 women are among c...
(2) There are four female custodians, but I don't know how many women there are in total out of all 120 employees.

By combining the two pieces of information, I can conclude that among all the 60 employees that are men or custodians, 4 of them are women. And since there are 60 women at the company, 56 of them will not be custodians.

Is this the correct thinking? I'd love some additional input!

chetan2u · Answer

hi,
these type of problems can be best solved through matrix...
let four categories of people in percentages be
a) m_c 
b) m_n_c 
c) f_c 
d) f_n_c .. we require to find this value
total=120..

1) statement 1 tells us.. m+c=50% 
 m_c + m_n_c + f_c + m_c =50%.
 m_c +(100%- f_n_c )=50%... 
 m_c +50%= f_n_c 
untill we know  m_c , we cannot find  f_n_c ... insufficient

2) statement 2 gives value of  f_c  as 4*100/120.... nothing much ..insufficient

combined we still cannot find the answer.. insufficient
ans E

peachfuzz · Answer

We know the number of males is (m/100)*120 and females is (1-m/100)*120. The number of custodial staff is (c/100)*120.

Statement 1:
we cannot relate m+c=50 to any of the information given.
Insufficient

Statement 2: 
female custodial staff = 4
Insufficient

Combined, there is still not enough information to relate any of the equations/info given.
Insufficient

Answer: E

OptimusPrepJanielle · Answer

Given that there are 120 employees.
m% are male, so (100-m)% are female.
Also, c% are custodians.
Let x MALE members and y FEMALE members be custodians.
So, x + y = c%

1) Using the first condition, we know that m + c = 50
m can take values from 0 to 50 and so there is no UNIQUE value of m. This implies there is no unique value c as well as f.
Since we don't have unique values, we cannot determine the required number of females.

2) Using the second condition, we know that female who are custodians are 4.
So, y = 4
But we don't know what x is. Hence we cannot know c.
So this condition also cannot give us an answer.

3) Using BOTH the conditions, we know that m + c = 50 and y = 4.
Once again, we cannot find x and hence we cannot find c.
So using both the conditions as well, we cannot identify the answer.

Hence (E).

--
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Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

(1) This statement could mean that, possibly, 40% of the employees are male and 10% of the employees are custodial, without any overlap (so that all custodians are female). Or, it could potentially mean that 40% are male and 10% are custodial, but that all of the custodians are male. Thus, this statement is insufficient.

(2) This statement gives us no information about the number of females who are not custodial, or about the number of female employees in total. Accordingly, statement 2 is insufficient.

Even when we use the statements together, we still cannot calculate any values except for the ones covered above. Since the two statements above do not provide sufficient information to answer the question, the correct answer is E.

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