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26 Mar 2018, 00:20
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
67% (03:04) correct
33%
(02:52)
wrong
based on 210
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 1/5
(B) 4/11
(C) 1/2
(D) 7/11
(E) 4/5
26 Mar 2018, 02:03
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Bunuel
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)
26 Mar 2018, 02:14
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Bunuel
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.
(D) is our answer.
