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

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29 Dec 2010, 11:59

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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?

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. _________________

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: In 2003, the number of girls attending Jefferson High School [#permalink]

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22 Jul 2014, 09:38

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.?

Re: In 2003, the number of girls attending Jefferson High School [#permalink]

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22 Jul 2014, 22:37

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.

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

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22 Jul 2014, 23:47

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

There is 1 key hint in this questions that will help you narrow down the answer.

"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.

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

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23 Jul 2014, 00:11

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)

Re: In 2003, the number of girls attending Jefferson High School [#permalink]

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23 Jul 2014, 00:15

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

There is 1 key hint in this questions that will help you narrow down the answer.

"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 _________________

Re: In 2003, the number of girls attending Jefferson High School [#permalink]

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03 Aug 2014, 00:21

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

D is the answer.

+1 Kudos if you guys like my answer. THanks _________________

......................................................................... +1 Kudos please, if you like my post

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Re: In 2003, the number of girls attending Jefferson High School
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03 Aug 2014, 00:21

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