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

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Joined: 02 Sep 2009
Posts: 51072
Mary is building a pyramid out of stacked rows of soup cans. When comp  [#permalink]

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05 Jul 2018, 03:57
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:56) correct 37% (02:01) wrong based on 49 sessions

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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

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Mary is building a pyramid out of stacked rows of soup cans. When comp  [#permalink]

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05 Jul 2018, 04:25
Bunuel wrote:
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

We are told that the top row of the pyramid that Mary is building will contain 1 soup can.
The second row contains 7(1+6) cans. Similarly, the third row contains 12(1+2*6) cans.

This is an arithmetic progression and sum of the terms is $$\frac{n}{2}(2a + (n-1)d)$$

Substituting values - n = 16, a = 1 and d = 7, the sum of terms is $$8(2 + 15*7) = 8*107 = 736$$
Therefore, Mary needs 736(Option C) cans to build the pyramid of soup cans.

Shortcut solution:
Units digits of the 16 digits is {1 + 7 + 3 + 9 + 5}3 times + 1 = 3*15 + 1 = 75 + 1 = 76
Since, the units digit is 6 and number of soup can's > 96. The answer option is 736(Option E)

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Re: Mary is building a pyramid out of stacked rows of soup cans. When comp  [#permalink]

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05 Jul 2018, 07:27
Bunuel wrote:
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

Row1 = 1
row 2 = 1 + 6
row 3 = 1 + 6*2
row 4 = 1 + 6*3
.
.
.
row 16 = 1 + 6 * 15

total cans = 16 + arithmetic sum of 6,12,18,....,90

= 16 + $$\frac{15}{2}$$(12 + 14 *6)

= 736

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Re: Mary is building a pyramid out of stacked rows of soup cans. When comp  [#permalink]

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03 Dec 2018, 19:38
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.

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Re: Mary is building a pyramid out of stacked rows of soup cans. When comp &nbs [#permalink] 03 Dec 2018, 19:38
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