In 2003, the number of girls attending Jefferson High School

Question

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

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

Mackieman · Answer

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

hirendhanak · Answer

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

KarishmaB · Answer

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.

PathFinder007 · Answer

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)

PathFinder007 · Answer

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

KarishmaB · Answer

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)

justbequiet · Answer

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.

PareshGmat · Answer

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. Answer = D = 5076

PareshGmat · Answer

It must be divisible by 12; 5058 is divisible by 6; but it yields a wrong answer. Refer explanation above

nhattruong1302 · Answer

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

vad3tha · Answer

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.

grassmonkey · Answer

Given that 2x is the student population in 2003 (as there are equal amounts of both boys and girls) then 2004 is:

2x*(6/5) = total
12x/5 = total
x =  /12

So the total has to be divisible by 12, which is the same as being divisible by 4 and 3. B, C, D are all divisible by 3 and D is the only one that is divisible by 4 (the last two digits are a multiple of 4).

(D)

ScottTargetTestPrep · Answer

We can let the number of girls in the school in 2003 = x = the number of boys in the school in 2003.

Therefore, the number of students in the school in 2004 is 1.2x + 1.2x = 2.4x. In order for this to be a whole number, x must be a multiple of 5, so we can let x = 5k where k is a positive integer, and 2.4x = 2.4(5k) = 12k. Therefore, we see that the total number of students in 2004 must be a multiple of 12.

Notice that 12 = 3 x 4; therefore, that number has to be divisible by 3 and 4. This eliminates choices B, C since they are not divisible by 4 (recall that a number is divisible by 4 if the last two digits of the number are divisible by 4). It also eliminates choices A and E since they are not divisible by 3 (recall that a number is divisible by 3 if the sum of the digits of the number is divisible by 3).

Thus, the only number that could be the total number of students in 2004 is choice D since it’s divisible by both 3 and 4 (notice that the sum of the digits = 5 + 0 + 7 + 6 = 18 and the last two digits are 76).

Answer: D

MAMannan · Answer

In 2003,
Girls (G) = Boys (B);

In 2004,
G = 1.2G and B = 1.2 B;

So, 1.2 G + 1.2 B = Total Students;
 or, 2.4 G (as G=B) = Total Students;
 or, G = Total students / 2.4;
Now test the options; the only D will come out with an integer.

ferhanhaider · Answer

Consider that
number of boys in 2003 = x 
=> number of girls in 2003 = x

In 2004, both increased by 20%(0.20), thus
number of boys in 2004 = 1.2x 
=> number of girls in 2004 = 1.2x
total = 1.2x + 1.2x = 2.4x => total =2.4x

so the total should be such that it's formed by multiplying a number with 2.4, which implies that the total should be divisible by 2.4

Among the answer choices, only D is divisible by 2.4

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In 2003, the number of girls attending Jefferson High School

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In 2003, the number of girls attending Jefferson High School

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards