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Of the 180 judges appointed by a certain President, 30 perc

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Of the 180 judges appointed by a certain President, 30 perc [#permalink] New post 23 Nov 2017, 12:10
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Of the 180 judges appointed by a certain President, 30 percent were women and 25 percent were from minority groups. If \(\frac{1}{9}\) of the women appointed were from minority groups, how many of the judges appointed were neither women nor from minority groups?

A. 75

B. 81

C. 87

D. 93

E. 99
[Reveal] Spoiler: OA

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Re: Of the 180 judges appointed by a certain President, 30 perc [#permalink] New post 26 Nov 2017, 02:10
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Explanation

We can use the formula: A+ B - N +B = 180 (Group A + Group B - Neither in the two groups + Both in the groups)

Women= \(180 * 0.3 = 54\)

Minority = \(180 * 0.25= 45\)

Women from minority group = \(54* \frac{1}{9} = 6\)

Back to the formula \(54 + 45 - 6 + B = 180\)

Both = \(87\)

C is the answer
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Re: Of the 180 judges appointed by a certain President, 30 perc [#permalink] New post 28 May 2018, 18:31
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Carcass wrote:
Of the 180 judges appointed by a certain President, 30 percent were women and 25 percent were from minority groups. If \(\frac{1}{9}\) of the women appointed were from minority groups, how many of the judges appointed were neither women nor from minority groups?

A. 75

B. 81

C. 87

D. 93

E. 99


We see that there are 180 x 0.3 = 54 women and 180 x 0.25 = 45 were from minority groups.

We also see that 54 x 1/9 = 6 women are from minority groups.

So we can create the equation:

Total = Women + Minority - Both + Neither

180 = 54 + 45 - 6 + Neither

87 = Neither

Answer: C
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Re: Of the 180 judges appointed by a certain President, 30 perc   [#permalink] 28 May 2018, 18:31
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