Of the 180 judges appointed by a certain

Of the 180 judges appointed by a certain President, 30 percent were women and 25 percent were from minority groups. If 1/9 of the women appointed were from minority groups, how many of the judges appointed were neither women nor from minority groups? 75, 81, 87, 93, 99

3 Explanations

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hi chris! I applied the formula of two overlapping sets which goes like this-
Total=group1+group2-(both g1 & g2) + (neither g1 and g2) and i got the answer 93. WHY is it wrong? here group1 will be women and group2 will be minority.
Please help.

Jul 13, 2017 • Comment

Sam Kinsman

Hi, happy to help! :)

You're on the right track - I think you just skipped a step at the end of the solution process.

Total = group 1 + group 2 - (both g1 & g2) + (neither g1 and g2)

180 = 54 + 45 - (6) + (neither g1 and g2)
180 = 93 + (neither g1 and g2)
87 = (neither g1 and g2)

So we know that 87 people were not women and not minorities. So in other words, there were 87 men who were not in minority groups. So the answer is C (87).

I hope this helps!

Jul 22, 2017 • Reply

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Robert Paul

I'm wondering if I should learn this box technique.

I first converted given percentages into actual number of amount of women and minority groups. Women = 180*0.3 = 54. Minority groups = 180*0.25= 45. 1/9th of women who were from minority groups were 54*0.1111(or 1/9)= 6. Then subtract this 6 from the minority group, because they already represented in the women group, giving you 39 (instead of 45) eligible individuals from minority groups.

39 (New minority group) + 54 women = 93 people who are either women or from minority groups

180 - 93 = 87 people who are neither women or from minority groups.

Sep 18, 2014 • Comment

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Chris Lele