sandy wrote:
When the number of people in an office is divided by 12, the remainder is 0. If \(\frac{3}{2}\) times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be
A. 1
B. 2
C. 3
D. 5
E. 6
Because division by 12 yields a remainder of 0, we see that the number of people in the office is a multiple of 12. We can multiply a few multiples of 12 by 3/2, and we have:
12 x 3/2 = 18 ---> 18/12 = 1 R 6
24 x 3/2 = 36 ---> 36/12 = 3 R 0
36 x 3/2 = 54 ---> 54/12 = 4 R 6
48 x 3/2 = 72 ---> 72/12 = 6 R 0
We see that when we divide those results by 12, we get a remainder of either 0 or 6. So, the only possible remainder that is greater than 0 is 6.
Answer: E