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In an office that employs 120 people, \(m\)% of the

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In an office that employs 120 people, \(m\)% of the

by BTGmoderatorLU » Fri Oct 25, 2019 2:25 am
Source: Veritas Prep

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.

The OA is E
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Source: — Data Sufficiency |
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by deloitte247 » Sun Oct 27, 2019 1:55 pm
Given that total employees = 120 people
m% are males and c% are custodial staff;
Total males = m%
Total females = (100 -m)%
Total employees = m% + (100 -m)%
120 = m% + (100 -m)%
Let male employees that are custodial staff = x
Let female employees that are custodial staff = y
Total custodial staff = c% =x + y
Female employees who are not members of the custodial staff = (total female) - (female that are custodial staff)
= (100 -m)% - y

Statement 1=> m + c = 50
If m = 10 and c = 40, then m+c = 50
If m = 30 and c = 20, then m+c = 50
The information available does not provide the unique value for 'm' and 'c', which will in turn affect the possible value of (100 -m)% and y.
Hence, statement 1 is NOT SUFFICIENT.

Statement 2=> The number of female employees who are members of the custodial staff is four.
Therefore, y = 4 but the value of m is still unknown, so, we cannot evaluate (100 -m)% - y.

Combining both statements;
Statement 1: m + c = 50
Statement 2: y = 4
Females who are not custodial staff = (100 -m)% - y.
If m=10 and c=40, then m+c = 50.
(100-m)% - y => (100-10)% - 5 => (90% of 120) - 4
If m=30 and c=20, then m+c = 50
(100-m)% - y => (100-30)% - 5 => (70% of 120) - 4
Since the value of m is not unique, then both statements combined together ARE NOT SUFFICIENT.

Answer = Option E

Thanks
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