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# In 2003, the number of girls attending Jefferson High School

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In 2003, the number of girls attending Jefferson High School [#permalink]  29 Dec 2010, 10:59
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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?

A. 4832
B. 5034
C. 5058
D. 5076
E. 5128
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 Sep 2013, 02:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: % change [#permalink]  29 Dec 2010, 14:59
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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, 19:57
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, 20:29
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Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 8169 Followers: 416 Kudos [?]: 111 [0], given: 0 Re: % change [#permalink] 20 Sep 2013, 02:27 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 10 Mar 2014 Posts: 232 Followers: 1 Kudos [?]: 41 [0], given: 13 Re: In 2003, the number of girls attending Jefferson High School [#permalink] 17 Jul 2014, 23:02 Here I did it in a following way. Lets assume in 2003 we have 100 students and both boys and girls are equal. total = 100 Boys = 50 girls = 50 now 20% increment in both boys and girls boys = 60 girls = 60 here total student = 120. we can say total 20% increment on 100 now we can say 6/5 x = value from options or x= 5/6 (value from option. Should be multiple of 6. only D fits in it) Manager Joined: 10 Mar 2014 Posts: 232 Followers: 1 Kudos [?]: 41 [0], given: 13 Re: In 2003, the number of girls attending Jefferson High School [#permalink] 22 Jul 2014, 08:38 VeritasPrepKarishma wrote: 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. HI Karishma, I have one query here. say we have x students (x= integer and x/2 is also an integer) now girls and boys are x/2 each. if we say 20 % increment means 6/5 x or we can say x = 5/6*options. Here c and d both are divided by 6. then how we will choose correct answer.? Thanks Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6219 Location: Pune, India Followers: 1675 Kudos [?]: 9588 [0], given: 197 Re: In 2003, the number of girls attending Jefferson High School [#permalink] 22 Jul 2014, 21:37 Expert's post PathFinder007 wrote: say we have x students (x= integer and x/2 is also an integer) now girls and boys are x/2 each. if we say 20 % increment means 6/5 x or we can say x = 5/6*options. Here c and d both are divided by 6. then how we will choose correct answer.? Thanks What you forgot to consider here is that x and x/2, both, should be integers. This means, after you divide the option by 6 and get x (after multiplying by 5 which doesn't matter), it should again be divisible by 2. Hence, the option must be successively divisible by 6 and 2 i.e. it must be divisible by 12 i.e by 3 as well as 4. We see that (C) and (D) are both divisible by 3. But only (D) is divisible by 4. Answer (D) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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In 2003, the number of girls attending Jefferson High School [#permalink]  22 Jul 2014, 22:47
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?

A. 4832
B. 5034
C. 5058
D. 5076
E. 5128

"In 2004, the population of girls and the population of boys both increased by 20 percent."

This means that $$New Population=\frac{6}{5}*Original population=New Population*\frac{5}{6}=*Original population$$
Since the number we are looking for is an integer, the number MUST BE divisible by 6.

Only Answer that will fulfill this requirement is D.
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In 2003, the number of girls attending Jefferson High School [#permalink]  22 Jul 2014, 23:11
PathFinder007 wrote:
VeritasPrepKarishma wrote:
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.

HI Karishma,

I have one query here.

say we have x students (x= integer and x/2 is also an integer)

now girls and boys are x/2 each.

if we say 20 % increment means 6/5 x or we can say x = 5/6*options.

Here c and d both are divided by 6. then how we will choose correct answer.?

Thanks

Not Karishma, but let's try

$$x = \frac{5}{6} * (options)$$ also

$$\frac{x}{2} = \frac{5}{12} * (options)$$ (Both conditions should satisfy)

Option C $$= \frac{5058}{6} = 843$$ >> 843 is a odd number; so it cannot be divided equally (No. of girls = No. of boys)

Also $$\frac{x}{2}$$ condition is not fulfilled

So option C = 5058 has to be ignored.

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Re: In 2003, the number of girls attending Jefferson High School [#permalink]  22 Jul 2014, 23:15
justbequiet wrote:
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?

A. 4832
B. 5034
C. 5058
D. 5076
E. 5128

"In 2004, the population of girls and the population of boys both increased by 20 percent."

This means that $$New Population=\frac{6}{5}*Original population=New Population*\frac{5}{6}=*Original population$$
Since the number we are looking for is an integer, the number MUST BE divisible by 6.

Only Answer that will fulfill this requirement is D.

It must be divisible by 12; 5058 is divisible by 6; but it yields a wrong answer. Refer explanation above
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Re: In 2003, the number of girls attending Jefferson High School [#permalink]  02 Aug 2014, 08:02
Be quick D

Girls = Boys = a

Number of students in 2014: 1,2*a + 1,2*a = 2,4*a

Now, we need an answer that could be divisible by 24= 3*2*2*2

Only B , C, D is divisible by 3, and only D is divisible by 4

Therefore, D is a correct answer for this question
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Re: In 2003, the number of girls attending Jefferson High School [#permalink]  02 Aug 2014, 23:21
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?

A. 4832
B. 5034
C. 5058
D. 5076
E. 5128

in 2003: G = B = x
in 2004: 1.2G = 1.2B = 1.2x
total student = 2.4x = 24*0.1*x = 3*4*2*0.1*x

so 3,4,2 must be the divisor of total number of students

A and E are eliminated since they cannot be divided by 3
B and C are eliminated since they cannot be divided by 4

+1 Kudos if you guys like my answer. THanks
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Re: In 2003, the number of girls attending Jefferson High School   [#permalink] 02 Aug 2014, 23:21
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