At an engineering firm, 80 employees have graduate degrees

[BTGmoderatorDC]

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.

OA C

Source: Veritas Prep

[swerve]

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.

OA C

Source: Veritas Prep

Phds only + Masters only + Both = 80.

Phds only + Both = ?

Statement 1: (1/3)Masters = Both \(\rightarrow\) Clearly insufficient. \(\Large{\color{red}\chi}\)

Statement 2: (1/2)Phds = Both \(\rightarrow\) Clearly insufficient. \(\Large{\color{red}\chi}\)

Combining 1 and 2, Masters = (3/2)Phds

(3/2)Phds + (1/2)Phds = 80 \(\rightarrow\) Phds = 40. Sufficient. \(\Large{\color{green}\checkmark}\)