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Job applicants - overlapping groups

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by BlueDragon2010 » Wed Feb 26, 2014 5:25 am
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
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by Patrick_GMATFix » Wed Feb 26, 2014 5:35 am
Overlapping sets can be solved in several ways; you could use Venn diagrams, the groups formula (total = group 1 + group 2 + neither - both), or use the groups table (also called a matrix). I go through the question in detail in the full solution below (taken from the GMATFix App).

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by Abhishek009 » Wed Feb 26, 2014 9:16 am
BlueDragon2010 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

Check the Diagram carefully , we are only interested in finding the Yellow Intersecting Part and nothing else...

Now calculate -

Candidates in total having Atleast 4 Years of Experience , Degrees and Less than 4 Years Experience is 14 + 18 + 3 = 35

However according to the Question the Total number of applicants who appeared for the Interview is 30

The this excess Counting ( 35 ) is due to the double Counting Error which we have overlooked ..

Hence the Yellow Intersecting Part is 35 - 30 = 5 Applicants...


Answer will be definitely be [spoiler](E)[/spoiler]
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by [email protected] » Wed Feb 26, 2014 6:18 pm
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).


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The answer to the question is in the upper-left corner: E

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Last edited by [email protected] on Wed Jan 11, 2017 11:11 am, edited 1 time in total.
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by Jeff@TargetTestPrep » Fri Jul 10, 2015 4:32 am
BlueDragon2010 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
Solution:

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

3) Had a degree

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

3) 18 applicants had degrees

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.

Image

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

Image

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.

Answer: E

Jeffrey Miller
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by Brent@GMATPrepNow » Fri Jul 10, 2015 7:00 am
Jeff's solution and the tic-tac-toe approach are also called the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of applicants , and the two characteristics are:
- least 4 years of experience or not least 4 years of experience
- has degree or doesn't have

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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