VJesus12 wrote: ↑Wed Nov 17, 2021 12:55 pm
At an engineering firm, 80 employees have graduate degrees (PhDs or Masters degrees). How many employees have PhDs?
(1) One-third of the employees with Masters degrees also have PhDs.
(2) One-half of the employees with PhDs also have Masters degrees.
Aswer:
C
Source: Veritas Prep
Given; At an engineering firm, 80 employees have graduate degrees (PhDs or Masters degrees).
Asked: How many employees have PhDs?
Let employees with PhD be P alone, employees with Masters be M alone and employees with PhD and Masters be PM.
\(P + M + PM = 80\)
\(Q. P + PM = ?\)
1) One third of the employees with Masters degrees also have PhDs.
\(1/3 (M+PM) = PM\)
\(PM = M 1/2\)
Since \(P\) is unknown. Not Sufficient \(\Large{\color{red}\chi}\)
2) One half of the employees with PhDs also have Masters degrees.
\(1/2(P+PM) = PM\)
\(P = PM\)
Since \(M\) is unknown. Not Sufficient \(\Large{\color{red}\chi}\)
Combining \(1 \& 2\)
1) One third of the employees with Masters degrees also have PhDs.
\(1/3 (M+PM) = PM\)
\(PM = M 1/2; M = 2PM\)
2) One half of the employees with PhDs also have Masters degrees.
\(1/2(P+PM) = PM\)
\(P = PM\)
\(P + M + PM = 80\)
\(P + 2P + P = 80\)
\(P = 20 = PM\)
\(P + PM = 40\) Sufficient \(\Large{\color{green}\checkmark}\)