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

Question

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.

Kurtosis · Answer

Phds only + Masters only + Both = 80.

Phds only + Both = ?

St1: (1/3)Masters = Both --> Clearly insufficient.

St2: (1/2)Phds = Both --> Clearly insufficient.

Combining St1 and St2, Masters = (3/2)Phds
(3/2)Phds + (1/2)Phds = 80 --> Phds = 40.
Sufficient.

Answer: C

Nunuboy1994 · Answer

Hey quick question- how did you get 3/2? What is the formula/ logic? I created a two circle venn diagram where A intersection B equals 1/2x and B (master's) equals 1/3? Did you divide 1/3 by 1/2? How did you know how to do this? I know it actually solves the question, after plugging in values in a different scenario, but still don't understand how you knew how to do that.

Push2018 · Answer

Combining statements (1) and (2):

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

bharathsaigal · Answer

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

If there is, please share the procedure.

Thanks!

almogsr · Answer

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

EncounterGMAT · Answer

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.

Kinshook · Answer

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

homersimpsons · Answer

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

kntombat · Answer

Even I have the same doubt  chetan2u   generis   Bunuel

TheBunk · Answer

Hi,

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

So neither = 0

chetan2u · Answer

Hi,

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

So neither is 0

KarishmaB · Answer

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.

achloes · Answer

bharathsaigal   EncounterGMAT

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