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Of 30 applicants for a job, 14 had at least 4 years'

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Of 30 applicants for a job, 14 had at least 4 years' [#permalink] New post 20 Dec 2012, 07:26
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Question Stats:

88% (02:17) correct 12% (01:27) wrong based on 202 sessions
Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?

(A) 14
(B) 13
(C) 9
(D) 7
(E) 5
[Reveal] Spoiler: OA
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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink] New post 20 Dec 2012, 07:28
Expert's post
Walkabout wrote:
Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?

(A) 14
(B) 13
(C) 9
(D) 7
(E) 5


Probably the easiest way to solve would be to make a matrix:
Attachment:
Experience.PNG
Experience.PNG [ 3.63 KiB | Viewed 2605 times ]
Note: numbers in black are given and numbers in red are calculated.

Answer: E.
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Of 30 applicants for a job, 14 had at least 4 years' experience, [#permalink] New post 14 May 2013, 15:27
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Step 1: assign variables to each of the data points provided in the question so that they correspond to the OVERLAPPING SETS formula:

30 = Total Applicants = T
14 = Applicants with 4 yrs exp = G1
18 = Applicants with degrees = G2
3 = Applicants with NEITHER 4yrs exp nor degrees = NONE
?? = Applicants with BOTH 4yrs exp AND degrees = BOTH

Step 2: recall the formula for overlapping sets with 2 groups: Total = G1 + G2 - BOTH + NONE

Step 3: Plug and chug the variables that we just assigned to solve for BOTH:
T = G1 + G2 - BOTH + NONE
30 = 14 + 18 - BOTH + 3
30 = 35 - BOTH
-5 = -BOTH
5 = BOTH

Correct Answer = E
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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink] New post 14 May 2013, 16:40
albertrahul wrote:
Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree.

(A) 14
(B) 13
(C) 9
(D) 7
(E) 5

Let's discuss.


Image

The set of 30 applicants is a square.

Applicants who have less than four years experience and also have no degree are outside both the circles. = 3 applicants.

Left circle denotes the number of applicants with at least 4years experience = A.

Right circle denotes the number of applicants with degrees = B.

Now number of applicants in both the circles should be 30 - 3. ie 27.

This 27 is equal to A + B - A intersection B.

We have to find A intersection B.

27 = 14 + 18 - A intersection B which gives A intersection B as 5
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Re: Of 30 applicants for a job, 14 had at least 4 years'   [#permalink] 14 May 2013, 16:40
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