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# The enrollment at a local private school for the new school year is 10

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
The enrollment at a local private school for the new school year is 10  [#permalink]

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25 Mar 2018, 23:20
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Difficulty:

65% (hard)

Question Stats:

66% (03:00) correct 34% (02:53) wrong based on 66 sessions

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The enrollment at a local private school for the new school year is 10% more than the enrollment at this time last year. The number of female students increased by 5%, and the number of male students increased by 20%. Female students make up what fraction of the current enrollment at the private school?

(A) 1/5
(B) 4/11
(C) 1/2
(D) 7/11
(E) 4/5

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The enrollment at a local private school for the new school year is 10  [#permalink]

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26 Mar 2018, 01:03
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Bunuel wrote:
The enrollment at a local private school for the new school year is 10% more than the enrollment at this time last year. The number of female students increased by 5%, and the number of male students increased by 20%. Female students make up what fraction of the current enrollment at the private school?

(A) 1/5
(B) 4/11
(C) 1/2
(D) 7/11
(E) 4/5

Let the total number of students be 300.
Since the enrollment saw a 10% increase, the enrollment for this new school year is 330

Now, the current male students are x and the current female students are 300 - x

The overall increase in enrollment is the sum of the increase in men and the increase in women
$$0.2x + 0.05(300 - x) = 30$$
$$0.20x + 15 - 0.05x = 30$$
$$0.15x = 15$$ -> x = $$\frac{15}{0.15} = 100$$

Therefore, the current female students are $$1.05*(200) = 210$$ and the percentage of female students is $$\frac{210}{330}$$ or $$\frac{7}{11}$$(Option D)
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The enrollment at a local private school for the new school year is 10  [#permalink]

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26 Mar 2018, 01:14
1
Bunuel wrote:
The enrollment at a local private school for the new school year is 10% more than the enrollment at this time last year. The number of female students increased by 5%, and the number of male students increased by 20%. Female students make up what fraction of the current enrollment at the private school?

(A) 1/5
(B) 4/11
(C) 1/2
(D) 7/11
(E) 4/5

We'll translate our question into equations so we understand what we need to do.
This is a Precise approach.

Say E is the original enrollment and m,f are the original numbers of males and females, respectively.
Then m + f= E and 1.2m + 1.05f = 1.1 E are our two equations.
We need to calculate 1.05f/1.1E so we'll use our two equations to cancel out m.
Multiplying the first equation by 1.2 gives 1.2m + 1.2f = 1.2E and subtracting the second equation from this gives
0.15f = 0.1E. Then E = 1.5f. So let's say f = 100, then E would equal 150.
1.05f = 105 and 1.1E = 165.
Then our ratio is 105/165 = 21/33 = 7/11.

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Re: The enrollment at a local private school for the new school year is 10  [#permalink]

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27 Mar 2018, 03:01
Bunuel, Would something like this work....

10% increase means that denominator is 11

Between 5% and 20% increase the total increase of 10% is close to the increase % of girls (weighted average principle). This means that girls number increased by a greater proportion.

So if I have to pick between 7/11 and 4/11 for girls, the answer is obviously 7/11
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Re: The enrollment at a local private school for the new school year is 10  [#permalink]

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27 Mar 2018, 10:35
Bunuel wrote:
The enrollment at a local private school for the new school year is 10% more than the enrollment at this time last year. The number of female students increased by 5%, and the number of male students increased by 20%. Female students make up what fraction of the current enrollment at the private school?

(A) 1/5
(B) 4/11
(C) 1/2
(D) 7/11
(E) 4/5

We can let the the enrollment last year = 100, so this year the enrollment is 1.1(100) = 110.

We can let the enrollment of female students last year = x, thus the enrollment of male students last year = 100 - x. Using the information given the problem, we can create the equation:

1.05x + 1.2(100 - x) = 110

1.05x + 120 - 1.2x = 110

-0.15x = -10

15x = 1000

x = 1000/15 = 200/3

Since the current total enrollment is 110 and the current enrollment of female students is 1.05 x 200/3 = 210/3 = 70, then the fraction of female students is 70/110 = 7/11.

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Re: The enrollment at a local private school for the new school year is 10   [#permalink] 27 Mar 2018, 10:35
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