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

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Joined: 18 Apr 2015
Posts: 5126
Followers: 76

Kudos [?]: 1028 [1] , given: 4631

Of the 180 judges appointed by a certain President, 30 perc [#permalink]  23 Nov 2017, 12:10
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Question Stats:

50% (02:27) correct 50% (04:08) wrong based on 2 sessions
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

_________________
Moderator
Joined: 18 Apr 2015
Posts: 5126
Followers: 76

Kudos [?]: 1028 [0], given: 4631

Re: Of the 180 judges appointed by a certain President, 30 perc [#permalink]  26 Nov 2017, 02:10
Expert's post
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 = $$87$$

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Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
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Kudos [?]: 117 [0], given: 0

Re: Of the 180 judges appointed by a certain President, 30 perc [#permalink]  28 May 2018, 18:31
Expert's post
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

_________________

Jeffery Miller

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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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