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The résumés of 40 people

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by mangomangodolly » Mon Nov 26, 2012 10:05 am
The résumés of 40 people who applied for a position requiring expertise in both math and English were summarized in a table. A checkrnark was entered in the math column for each person with a degree in math and in the English column for each person with a degree in English. In the table, 50% of the people had checkrnarks in the math column, 15% had checkrnarks in both the math and English columns, and 5% had checkmarks in neither column. How many of the 40 people had checkrnarks in the English column?

A. 6
B. 14
C. 18
D. 20
E. 24
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by granite » Mon Nov 26, 2012 11:18 am
You can either draw out a Venn diagram or use the formula [Grp 1 + Grp 2 - Both + Neither]. We know the formula has to equal 40 since it's given there were 40 applicants. I converted the percents to real numbers before plugging them into the equation (example 50% of 40 is 20).

Grp 1 = English
Grp 2 = Math

20 + Grp 2 - 6 +2 = 40

Solve for Grp 2 to get 24. Choose answer E.

You can work backwards to confirm the answer.
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by Bill@VeritasPrep » Mon Nov 26, 2012 11:15 pm
You could also solve by adding the percentages:

Math-only + English-only + Both + Neither = 100%

Since the 50% in Math includes those with only math and those with both, we can subtract the 15% for Both to get 35% for Math-only. We have:

35% + English-only + 15% + 5% = 100%

English-only then has to be 45%.

This means that 60% of the people have a checkmark in the English column, and 60% * 40 = 24.
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