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At Laurent Hills Elementary, if 60% of the 2000 students participate

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At Laurent Hills Elementary, if 60% of the 2000 students participate  [#permalink]

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New post 11 Jan 2018, 23:21
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At Laurent Hills Elementary, if 60% of the 2000 students participate in after school activities. What percent of the students at the school are male?

(1) The number of female students who do not participate in after school activities is twice the number of male students who participate in after school activities.
(2) The number of female students who do not participate in after school activities is three times the number of male students who do not participate in after school activities.

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Re: At Laurent Hills Elementary, if 60% of the 2000 students participate  [#permalink]

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New post 16 Jan 2018, 00:04
Bunuel wrote:
At Laurent Hills Elementary, if 60% of the 2000 students participate in after school activities. What percent of the students at the school are male?

(1) The number of female students who do not participate in after school activities is twice the number of male students who participate in after school activities.
(2) The number of female students who do not participate in after school activities is three times the number of male students who do not participate in after school activities.


So here we have 4 kinds of people: Males who participate, Females who participate, Males who dont participate, Females who dont participate. Let me call these 4 categories as MP, FP, MNP, FNP respectively. We are given that MP + FP = 60% of 2000 = 1200. Thus MNP + FNP = 2000-1200 = 800. We need to find MP + MNP (total males) as a percentage of 2000.
MP + MNP will give us the number of males. FP + FNP will give us the number of females.

(1) FNP = 2*MP. Let MP = x, then FNP = 2x. This will give FP = 1200-x and MNP = 800-2x. So total number of males = x + 800 - 2x = 800+x. But we dont have the value of x, so we cannot find the answer. Insufficient.

(2) FNP = 3*MNP. And their sum should be 800 (non participants). This gives us MNP=200 and FNP=600. But we dont have the value of MP so we cannot find the number of males. Insufficient.

Combining the two statements, MNP=200, FNP=600 and from first statement, FNP=2*MP, so MP=300. This will give us MNP + MP = 200+300 = 500. And now we can find the desired percentage. Sufficient.

Hence C answer
Re: At Laurent Hills Elementary, if 60% of the 2000 students participate &nbs [#permalink] 16 Jan 2018, 00:04
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