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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