Problem Solving

Gmat_mission wrote: ↑

Tue Nov 10, 2020 8:17 am

\(P =\{6, 3, 0, d, 4, 14, 9, 2d\}\)

If \(d\) is the smallest positive integer such that the range of the remainders obtained when multiples of \(3\) are divided by \(d\) is \(3,\) by what percentage is the median of the numbers in \(P\) smaller than the mean of the numbers in \(P?\)

A. \(11.1\%\)
B. \(12.5\%\)
C. \(16.7\%\)
D. \(20.0\%\)
E. Cannot Be Determined

Answer: C

Solution:

We see that d must be 4 since the smallest remainder when a multiple of 3 is divided by 4 is 0 (for example, 12/4 = 3 R 0) and the largest remainder when a multiple of 3 is divided by 4 is 3 (for example, 3/4 = 0 R 3). Therefore, P = {6, 3, 0, 4, 4, 14, 9, 8} or {0, 3, 4, 4, 6, 8, 9, 14}. We see that the median of the numbers in P is (4 + 6)/2 = 5 and the mean of the numbers in P is (0 + 3 + 4 + 4 + 6 + 8 + 9 + 14)/8 = 48/8 = 6. Since 5 is 1 less than 6, we see that 5 (the median) is 1/6 or 16.7% less than 6 (the mean).

Answer: C