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Mary is building a pyramid out of stacked rows of soup cans.

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Mary is building a pyramid out of stacked rows of soup cans.

by AAPL » Mon Dec 03, 2018 5:22 am

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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.
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by [email protected] » Mon Dec 03, 2018 11:24 am
Hi All,

We're told that Mary is building a pyramid out of stacked rows of soup cans; the top row of the pyramid contains a single soup can, each row below the top row contains 6 MORE cans than the one above it and the completed pyramid contains 16 rows. We're asked for the TOTAL number of soup cans the pyramid. This question can be solved with a bit of Arithmetic and "bunching."

To start, we can list out the first few terms in this sequence: 1, 7, 13, 19, 25...... each term increases by 6, so we can determine the 16th term (re: the last term) in the sequence 1 + (15)(6) = 1 + 90 = 91.

Next, since the increase is a constant, we can 'bunch' the largest and smallest terms in the sequence and define a pattern:
1 + 91 = 92
7 + 85 = 92
13 + 79 = 92
Etc.

We'll end up with 8 'pairs' of 92, so the total number of cans is (8)(92) = 736.

Final Answer: E

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Mary is building a pyramid out of stacked rows of soup cans.

by fskilnik@GMATH » Mon Dec 03, 2018 4:49 pm
AAPL wrote:Princeton Review

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.
$$?\,\,\, = \,\,\,\# \,\,{\rm{soup}}\,\,{\rm{cans}}$$
The number of soup cans constitute a finite arithmetic sequence, hence the average number of cans per row is equal to M = (1+N)/2 ,
where N is the number of cans in the 16th row, that is, 1+15*6 = 91. Hence:
$$M = {{1 + 91} \over 2}\,\,\,\, \Rightarrow \,\,\,\,? = 16 \cdot \left( {{{1 + 91} \over 2}} \right) = 8 \cdot 92 = 736$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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