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

Question

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

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

pushpitkc · Answer

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)

LordStark · Answer

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

answer E

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

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

fireagablast · Answer

Math is wrong here..
Number of cans added per row is 6, not 7.
16/2*(2(1)+(16-1)6)
8*(2+90)
8*92 = 736

effatara · Answer

We can form an arithmetic series of 16 terms with each term representing the number of cans in each row starting with the bottom row. The nth term of an arithmetic series is given by:
nth term (1 in this case) = a + (n-1)d where 'a' is the first term (# of cans in the bottom row), 'n' the total number of terms in the series (16 in this case) and 'd' the common difference (which is -6 in this case since the number of cans in each row is 6 less than the preceding one). Thus:
1 = a + (16 -1)(-6)....> a = 91.
The total number of cans in the pyramid is obviously the sum of the series which is given by:
Sum = (half the total # of terms)(1st term + last term) = 8*(91 +1) = 736.
ANS: E

EgmatQuantExpert · Answer

Solution

Given

• A pyramid is formed in such a way that each row contains 6 cups more than the previous row.
• The First row contains 1 cup and there are 16 rows.

To Find 
 • Total number of cups to be used.

Approach and Working Out

From the information given we can infer that the number of cups
  o In the second row will be 1 + 6 = 1 + 6 × 1 
o In the third row it’s 1 + 6 + 6 = 1 + 6 × 2 and so on,

We will have a series as
  o 1, 1 + 1 × 6, 1 + 2 × 6, … , 1 + 15 × 6

• The average of the above series is  \frac{(first term + last term)}{2} 
  =  \frac{(1 + 91)}{2} 
 = 46 
 
 • Number of terms = 16
• Summation = 16 × 46 = 736

Correct Answer: Option E

bumpbot · Answer

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

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