Mary is building a pyramid out of stacked rows of soup cans. When completed, the top row of the pyramid contains a

[BTGmoderatorDC]

Mary is building a pyramid out of stacked rows of soup cans. When completed, the top row of the pyramid contains a single soup can, and each row below the top row contains 6 more cans than the one above it. If the completed pyramid contains 16 rows, then how many soup cans did Mary use to build it?

A. 91
B. 96
C. 728
D. 732
E. 736


OA E

Source: Princeton Review

[swerve]

Mary is building a pyramid out of stacked rows of soup cans. When completed, the top row of the pyramid contains a single soup can, and each row below the top row contains 6 more cans than the one above it. If the completed pyramid contains 16 rows, then how many soup cans did Mary use to build it?

A. 91
B. 96
C. 728
D. 732
E. 736


OA E

Source: Princeton Review

Row 1 \(= 1\)
Row 2 \(= 1 + 6\)
Row 3 \(= 1 + 6 \cdot 2\)
Row 4 \(= 1 + 6 \cdot 3\)
.
.
.
Row 16 \(= 1 + 6 \cdot 15\)

Total cans \(= 16 +\) arithmetic sum of \(6,12,18,\cdots,90\)

\(= 16 + \frac{15}{2}(12 + 14 \cdot 6)\)
\(= 736\)

Therefore, E

[Scott@TargetTestPrep]

Mary is building a pyramid out of stacked rows of soup cans. When completed, the top row of the pyramid contains a single soup can, and each row below the top row contains 6 more cans than the one above it. If the completed pyramid contains 16 rows, then how many soup cans did Mary use to build it?

A. 91
B. 96
C. 728
D. 732
E. 736


OA E

Solution:


Counting the rows from top to bottom, the number of cans in each row is :

1st row = 1

2nd row = 1 + 6 = 7

3rd row = 1 + 2(6) = 13

4th row = 1 + 3(6) = 19

and so on. So the last row, the 16th row, must have 1 + 15(6) = 91 cans. Since the number of cans in each row forms an evenly spaced set, we can use the following formula to find the total number of cans:

Sum = (1st row + last row)/2 x number of rows

Therefore, there are a total of (1 + 91)/2 x 16 = 92 x 8 = 736 cans in the pyramid.

Answer: E