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

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

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Mary is building a pyramid out of stacked rows of soup cans. [#permalink] New post 27 Mar 2018, 16:15
Expert's post
00:00

Question Stats:

33% (02:22) correct 66% (00:00) wrong based on 3 sessions
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

Drill 3
Question: 9
Page: 547-548
[Reveal] Spoiler: OA

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Sandy
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Intern
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Joined: 02 Aug 2017
Posts: 24
Followers: 1

Kudos [?]: 12 [0], given: 4

Re: Mary is building a pyramid out of stacked rows of soup cans. [#permalink] New post 27 Mar 2018, 21:27
lets number each row starting from top as 16th row.
then,
16th row contains 1 can.
15th row contains (1+6) cans.
14 th row contains (1+6*2) cans.
so on
2nd row contains (1+6*14) cans
1st row contains (1+6*15) cans

so summing up all
total cans is equal to
=16th +15th+14th+......+2nd +1st rows cans
=1*16+(1+2+3+....+14+15)*6
=16+15*16*6/2 sum of n natural no is n(n+1)/2
=15+720
=736 ans.


ans= E
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

CAT Tests
Re: Mary is building a pyramid out of stacked rows of soup cans. [#permalink] New post 28 Mar 2018, 13:38
Expert's post
Explanation

The top row contains 1 can, the second row contains 1 + 1(6) = 7 cans, the third row contains 1 + 2(6) = 13 cans, and so forth, so that the sixteenth row contains 1 + 15(6) = 91 cans.

But you need to find the total number of cans, which is 1 + 7 + 13 +…+ 79 + 85 + 91. Notice that adding the first and last term in the sequence gives you 92. Adding the second and second to last term also gives you 92: As you move to the next term at the beginning of the sequence, you are adding 6, while as you move to the previous term at the end of the sequence, you are subtracting 6, so the sum will remain constant.

Thus, for each pair of rows, the sum is 92. Sixteen rows represents eight pairs of rows, so the total number of cans is (8)(92) = 736. The answer is choice (E).
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Re: Mary is building a pyramid out of stacked rows of soup cans.   [#permalink] 28 Mar 2018, 13:38
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Mary is building a pyramid out of stacked rows of soup cans.

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