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

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Math Expert
Joined: 02 Sep 2009
Posts: 52392
At an engineering firm, 80 employees have graduate degrees (PhDs or Ma  [#permalink]

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09 Feb 2017, 02:14
1
4
00:00

Difficulty:

65% (hard)

Question Stats:

64% (01:57) correct 36% (01:48) wrong based on 136 sessions

### HideShow timer Statistics

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.

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Re: At an engineering firm, 80 employees have graduate degrees (PhDs or Ma  [#permalink]

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10 Feb 2017, 09:50
1
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.

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Re: At an engineering firm, 80 employees have graduate degrees (PhDs or Ma  [#permalink]

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23 Mar 2017, 14:45
Vyshak wrote:
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.

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.
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Re: At an engineering firm, 80 employees have graduate degrees (PhDs or Ma  [#permalink]

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24 Mar 2017, 08:54
Nunuboy1994 wrote:
Vyshak wrote:
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.

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.

Combining statements (1) and (2):

1/3M=1/2 PhDs
M=3/2PhDs
Re: At an engineering firm, 80 employees have graduate degrees (PhDs or Ma &nbs [#permalink] 24 Mar 2017, 08:54
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