At an engineering firm, 80 employees have graduate degrees (PhDs or Ma

Combining statements (1) and (2):

1/3M=1/2 PhDs
M=3/2PhDs

Is there a way to solve this question using table form?

If there is, please share the procedure.

Thanks!

can you have a PHD without a Master? makes no sense... got confused over it

Tried to solve the question by 2x2 matrix but in vain. After a lot of brainstorming (and research lol), here's how I solved. Hope it helps.

Let Ph.D be p and Masters be m.

p+m-both=80 and p=?

(1) One third of the employees with Masters degrees also have PhDs.
\(\frac{1}{3}\) of m also have p. Means \(\frac{1}{3}\) of m have both. => \(\frac{1}{3}\)m=both => m=3both

p + 3both + both = 80 => 4both+p=80............nothing about p. INSUFFICIENT!

(2) One half of the employees with PhDs also have Masters degrees.
\(\frac{1}{2}\) of p also have m. Means \(\frac{1}{2}\) of p have both. => \(\frac{1}{2}\)p=both => p=2both

2both + m + both = 80 => 3both+m=80............nothing about m. INSUFFICIENT!

(1) + (2)
m=3both and p=2both

Therefore, 2both+3both-both=80 => both=20
p=2(20) = 40

Answer is option C.

P.S: anyone who could solve this question by 2x2 matrix, please post it.

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

(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

(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

IMO C

Phds only + Masters only + Both = 80.
Wouldn't this formula change to
Phds only + Masters only + Both + Neither = 80.
And since no information is given about neither we don't have sufficient information.
So answer should be E.
VeritasKarishma generis chetan2u

Even I have the same doubt chetan2u generis Bunuel

Hi,

You are told in the question that the 80 employees either have a PHd or a Master's degree.

So neither = 0

Hi,

The question the way it is written means that Graduate degree is in just two cases - masters and phd

So neither is 0

homersimpsons:

The question says:
At an engineering firm, 80 employees have graduate degrees (PhDs or Masters degrees).

The graduate degrees are defined as PhDs and Masters. So when they say 80 employees have graduate degrees, it means 80 employees have PhDs or Masters.
Hence none = 0.

bharathsaigal EncounterGMAT