In an office that employs 120 people, $m$% of the

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BTGmoderatorLU: Moderator; Posts: 2547; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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: Beat The GMAT — Data Sufficiency | Fri Oct 25, 2019 2:25 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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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