A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton...

[BTGmoderatorLU]

Source: Economist GMAT

A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour, he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total of 450 kilos of plankton, how many kilos did he consume on the sixth hour?

A. 38
B. 47
C. 50
D. 53
E. 62

The OA is D

[Scott@TargetTestPrep]

Source: Economist GMAT

A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour, he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total of 450 kilos of plankton, how many kilos did he consume on the sixth hour?

A. 38
B. 47
C. 50
D. 53
E. 62

The OA is D

Since the whale consumes x kilos of plankton in the first hour, the number of kilos of plankton consumed in: the second hour = x + 3, in the third hour = x + 6, ..., and in the last (or 9th) hour = x + 24. Recalling that average * quantity = sum, we can create the equation:

[x + (x + 24)]/2 * 9 = 450

(2x + 24)/2 = 50

2x + 24 = 100

2x = 76

x = 38

Since the sixth hour = x + 15, the whale consumes 38 + 15 = 53 kilos of plankton in the sixth hour.

Answer: D