BTGmoderatorLU wrote: ↑

Fri Mar 05, 2021 3:01 am

Source: Manhattan Prep

A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set?

A. 85
B. 86
C. 88
D. 91
E. 92

The OA is E

Solution:

We are given that a set of 5 numbers has an average of 50. Thus, the set has a sum of 250.
We are also given that the largest element in the set is 5 greater than 3 times the smallest element in the set. If we let the smallest element = x, then the largest element is 3x + 5. Finally since the median = average, the median = 50. To determine the largest possible value in the set, let’s minimize the first four values.
1st value = x
2nd value = x
3rd value = median = 50
4th value = 50
5th value = 3x + 5
Thus:
x + x + 50 + 50 + 3x + 5 = 250
5x + 105 = 250
5x = 145
x = 29
It follows that the largest value is 3 x 29 + 5 = 92.

Answer: E