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# % change

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% change [#permalink]  29 Dec 2010, 11:59
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Question Stats:

62% (02:39) correct 37% (05:16) wrong based on 0 sessions
In 2003, the number of girls attending Jefferson High School was equal to the number of boys. In 2004, the population of girls and the population of boys both increased by 20 percent. Which of the following could be the total student population at Jefferson High School in 2004?

4832
5034
5058
5076
5128
[Reveal] Spoiler: OA

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Re: % change [#permalink]  29 Dec 2010, 15:59
Total number of students Y 2004 (B = boys per 2003 and G = girls per 2003)
Y = B*1.2 +G*1.2
Y = 2.4B (since B=G)
B = Y/2.4 => B= 10Y/24

Factors = 24, 12, 8, 6, 4, 3, 1
Our answer will be divisible by all these factors without leaving a remainder

First,

A)4+8+3+2 = 17 (not divisble by three = out)
B)5+0+3+4 = 12
C)5+0+5+8 = 18
D)5+0+7+6 = 18
E)5+1+2+8 = 16 (not divisible by three = out)

B,C,E left

If the two last digits are divisible by four so will the whole number

34/4 = not integer
58/4 = not integer
76/4 = 60 + 16 = 15*4 + 4*4 = 19

D = correct
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Re: % change [#permalink]  29 Dec 2010, 20:57
the fig of 2004 is 120 (60+60) ( if we consider the fig of 2003 as 100 ( 50+50) )

now ideally 120 is ( 6 parts of 20 each , we require 5 parts of 20 to make it 100) , so the answer must be divisible by 6

B,C and D are left , dividing each with 6 brings (839,843 and 846) which is one part (20%) and we require five parts to make it to 100 ( 2003 population)

the no must be even since it is boys + girls - 839*5 and 843*5 are singular, so the best solution is D
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Re: % change [#permalink]  29 Dec 2010, 21:29
shrive555 wrote:
In 2003, the number of girls attending Jefferson High School was equal to the number of boys. In 2004, the population of girls and the population of boys both increased by 20 percent. Which of the following could be the total student population at Jefferson High School in 2004?

4832
5034
5058
5076
5128

Let number of boys = number of girls = a (An integer)
Total number of students = 2a
New total number of students = (6/5)*2a (Since each a increased by 20%, the total will increase by 20% i.e. an increase of 1/5)

Now (12/5)*a is the answer i.e. (12/5)*a = 4832 or 5034 or 5058 etc....
or a = Answer Option * 5/12
The only restriction is that 'a' should be an integer. So the answer option must be divisible by 12.
Check the options: Which one is divisible by both 3 and 4? Only 5076.
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Re: % change   [#permalink] 29 Dec 2010, 21:29
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