In 2003, the number of girls attending Jefferson High School

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.

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)

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

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)

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.

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

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

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

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

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 = [(total)*5]/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)

Hi Karishma,

Why are we not checking the numbers in the option for being a multiple of 5?

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

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.

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

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