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The School of Architecture at Augury University had...

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The School of Architecture at Augury University had...

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The School of Architecture at Augury University had 300 applicants this year. Of these applicants two-thirds had previous experience working in an architectural office and two-fifths had extensive artistic portfolios. If one-third of the applicants had neither extensive portfolios nor work experience in an architectural office then how many of the applicants had both extensive portfolios and work experience in an architectural office?

A. 200
B. 120
C. 100
D. 80
E. 20

The OA is B.

Please, can any expert help me with this PS question? I don't have it clear. Thanks.

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GMAT/MBA Expert

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Hello.

Let's see the hypothesis step by step.

Total of applicants: 300.

- two-thirds had previous experience working in an architectural office: this is equivalent to $$\frac{2}{3}\cdot300=200\ applicants.$$

- two-fifths had extensive artistic portfolios: this is equivalent to $$\frac{2}{5}\cdot300=120\ applicants.$$

- one-third of the applicants had neither extensive portfolios nor work experience in an architectural office: this is equivalent to $$\frac{1}{3}\cdot300=100\ applicants.$$

So, all the applicants who had extensive artistic portfolios also had previous experience working in an architectural office, this is 120.

The correct answer is B.

I hope this explanation can help you.

I'm available if you'd like a follow up.

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This problem involves two overlapping sets (experience vs. no experience and portfolio vs. no portfolio), so we should immediately start making a double matrix. Double matrices help us to organize the information we have so we know what we can and can't figure out. (Note: if we have more than two overlapping sets, a Venn Diagram is probably your best bet.)

So we start by making our matrix:



Note that we filled in 1 for the Total number of applicants since we are dealing with fractions.

Then we fill in what we know from the problem:



In a double matrix, the top two cells in each column should add up to the total in the bottom cell in the column, and the leftmost two cells in each row should add up to the total in the rightmost cell in the row. This means that if we have two cells in one row or two cells in one columns, we can use that information in the table to fill in the third cell. Let's see what else we can determine in our table:



then



and finally



So 2/5 of the applications have both experience and a portfolio. There are 300 total applicants, so 2/5 * 300 = 120.

Note: We didn't actually need to solve for all of the cells in this problem - we only need to solve for enough to get the top left cell (both experience and portfolio). This means we could have gotten away without solving for experience and no portfolio, which would have saved us time converting to fifteenths.

Note 2: You *can* do this kind of problem in your head, but I highly recommend using some sort of diagram to keep track of your information. They're easy to draw on your scratch pad, and they keep you from getting all of those numbers and relationships mixed up.

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