In 2003, the number of girls attending Jefferson High

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?

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

The OA is the option D.

How can I find the population in 2004 if I don't know the population in 2003? Could anyone clarify this for me? Thanks.

GMATGuruNY · Answer

M7MBA 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

Test the SMALLEST POSSIBLE CASE.

Since both populations increase by 20% = 1/5, the original number of boys and the original number of girls must each be a multiple of 5.
Since in 2003 there must be an equal number of boys and girls, the smallest possible case is as follows:
2003: boys = 5 and girls = 5
2004: boys = 5 + (1/5)5 = 6 and girls = 5 + (1/5)5 = 6, for a total of 12 students.

The result in blue implies that the total number of students in 2004 must be a MULTIPLE OF 12.
For a number to be a multiple of 12, it must be divisible by both 4 and 3.

A number is divisible by 4 only if its last two digits form an integer that can divided twice by 2.
Of the five answer choices, only A, D and E satisfy this condition:
A: 32 --> 16 --> 8
D: 76 --> 38 --> 19
E: 28 --> 14 --> 7
Eliminate B and C.

A number is divisible by 3 only its digits sum to a multiple of 3.
Of the three remaining answer choices, only D works:
5+0+7+6 = 18, which is a multiple of 3.
Eliminate A and E.

The correct answer is D.

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Scott@TargetTestPrep · Answer

M7MBA 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

Test the SMALLEST POSSIBLE CASE.

Since both populations increase by 20% = 1/5, the original number of boys and the original number of girls must each be a multiple of 5.
Since in 2003 there must be an equal number of boys and girls, the smallest possible case is as follows:
2003: boys = 5 and girls = 5
2004: boys = 5 + (1/5)5 = 6 and girls = 5 + (1/5)5 = 6, for a total of 12 students.

The result in blue implies that the total number of students in 2004 must be a MULTIPLE OF 12.
For a number to be a multiple of 12, it must be divisible by both 4 and 3.

A number is divisible by 4 only if its last two digits form an integer that can divided twice by 2.
Of the five answer choices, only A, D and E satisfy this condition:
A: 32 --> 16 --> 8
D: 76 --> 38 --> 19
E: 28 --> 14 --> 7
Eliminate B and C.

A number is divisible by 3 only its digits sum to a multiple of 3.
Of the three remaining answer choices, only D works:
5+0+7+6 = 18, which is a multiple of 3.
Eliminate A and E.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

swerve · Answer

Let's 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 students = 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).

Regards!

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