Of 30 applicants for a job, 14 had at least 4 years' : GMAT Problem Solving (PS)
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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]

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20 Dec 2012, 07:26
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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]

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20 Dec 2012, 07:28
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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 [ 3.63 KiB | Viewed 10045 times ]
Note: numbers in black are given and numbers in red are calculated.

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Of 30 applicants for a job, 14 had at least 4 years' experience, [#permalink]

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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

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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink]

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14 May 2013, 16:40
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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.

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]

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07 Oct 2014, 05:57
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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink]

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19 Nov 2015, 05:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink]

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19 Nov 2015, 10:12
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

Working same as Bunuel, still sahring
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Degree and Experience.PNG [ 3.69 KiB | Viewed 3950 times ]

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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink]

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19 Nov 2015, 16:19
Hi BlueDragon2010,

Each of the responses presents a variation on the solution. Here's one that uses the Tic-Tac-Toe board.

The initial 3x3 grid contains the information given by the prompt.

The second 3x3 grid contains the first set of deductions (the sub-totals, in blue), followed by the sub-groups (in green).

http://postimg.org/image/h4gg5bmu5/

The answer to the question is in the upper-left corner:
[Reveal] Spoiler:
A

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Re: Of 30 applicants for a job, 14 had at least 4 years' [#permalink]

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07 Jul 2016, 08:24
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

For this we can setup a table with 2 main categories: years of experience and degrees. These can be broken down further into:

1) Had at least 4 years of experience

2) Had less than 4 years of experience

4) Did not have a degree

In addition we are given the following information:

1) There are 30 total applicants

2) 14 applicants had at least 4 years of experience

4) 3 applicants had less than 4 years of experience and did not have a degree

Let’s fill all this information into a table.

We can use the information to fill in the rest of the chart. Remember the “Total” label in each column or row represents the sum of the preceding two cells in each column or row, respectively.

We are asked how many of the applicants had at least 4 years' experience and a degree. We can see from our table that the answer is 5.

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Re: Of 30 applicants for a job, 14 had at least 4 years'   [#permalink] 07 Jul 2016, 08:24
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