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
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