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# At Markham Academy, 2/3 of the m faculty members live in housing on ca

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
At Markham Academy, 2/3 of the m faculty members live in housing on ca  [#permalink]

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18 Feb 2019, 04:16
00:00

Difficulty:

5% (low)

Question Stats:

92% (01:31) correct 8% (01:27) wrong based on 38 sessions

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At Markham Academy, 2/3 of the m faculty members live in housing on campus grounds. Of those living on campus, 3/4 own a car. Which of the following represents, in terms of m, the number of faculty members who live in campus housing and do not own a car?

A. m/4
B. m/6
C. m/12
D. 2m/3
E. 3m/4

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Re: At Markham Academy, 2/3 of the m faculty members live in housing on ca  [#permalink]

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18 Feb 2019, 04:25
Bunuel wrote:
At Markham Academy, 2/3 of the m faculty members live in housing on campus grounds. Of those living on campus, 3/4 own a car. Which of the following represents, in terms of m, the number of faculty members who live in campus housing and do not own a car?

A. m/4
B. m/6
C. m/12
D. 2m/3
E. 3m/4

solved using 2x2 grid
let m = 12
so not owning a car and living in campus ; 2
i.e m/6 ; IMO B
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Re: At Markham Academy, 2/3 of the m faculty members live in housing on ca  [#permalink]

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18 Feb 2019, 04:42
m=LCM(3,4)=12
2/3m= 8
3/4of8=6
faculty with car=2
2/12=1/6

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Re: At Markham Academy, 2/3 of the m faculty members live in housing on ca  [#permalink]

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18 Feb 2019, 05:25
faculty in campus =$$\frac{2m}{3}$$
who own a car$$\frac{2}{3}*\frac{3}{4}* m$$
=$$\frac{m}{2}$$
Thus who dont a car and live in camous =$$\frac{2m}{3}- \frac{m}{2}$$= $$m/6$$
Re: At Markham Academy, 2/3 of the m faculty members live in housing on ca   [#permalink] 18 Feb 2019, 05:25
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