In a certain supermarket, a triangular display of cans is ar

gmat_guy666 wrote:In a certain supermarket, a triangular display of cans is arranged in 8 rows, numbered 1 through 8 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 95 cans in the entire display, how many cans are in the fifth row?

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OA [spoiler]C
[/spoiler]

Hmmm,

Let's see what happens if there's 1 can in the top (1st) row.
Row #1: 1 can
Row #2: 4 cans
Row #3: 7 cans
Row #4: 10 cans
Row #5: 13 cans

Done.
Answer: C

Cheers,
Brent

gmat_guy666 wrote:In a certain supermarket, a triangular display of cans is arranged in 8 rows, numbered 1 through 8 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 95 cans in the entire display, how many cans are in the fifth row?


10


11


13


14


16

OA [spoiler]C
[/spoiler]

We can let x = the number of cans in the first row. Thus, x + 3, x + 2(3), …, x + 7(3) are the number of cans in the second, third, …, eighth rows, respectively. Since we have an evenly spaced set, we can use the formula sum = avg * quantity where:

Avg = (largest number + smallest number)/2
Quantity = 8

We can create the inequality:

sum < 95

avg * quantity < 95

(x + 7(3) + x)/2 * 8< 95

(2x + 21)/2 * 8 < 95

(2x + 21) * 8 < 190

16x + 168 < 190

16x < 22

x < 22/16

Since x must be a whole number, x = 1. Therefore, the number of cans in the fifth row is x + 4(3) = 1 + 12 = 13.

Answer: C