Brick wall

The solution below is taken from the GMATFix App.



-Patrick

GmatGreen wrote:In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

A) 14
B) 15
C) 16
D) 17
E) 18

Since the number of bricks per row keeps decreasing by 1, the total number of bricks -- 75 -- is the sum of 5 consecutive integers.
We can PLUG IN THE ANSWERS, which represent the number of bricks in the bottom row.

Since the total number of bricks is ODD, the correct answer choice cannot be even, since an even number of bricks on the bottom row will yield an even sum:
even + odd + even + odd + even = even.
Eliminate A, C and E.

The AVERAGE number of bricks per row = 75/5 = 15.
Since the bottom row must contain the GREATEST number of bricks, the number of bricks on the bottom row must be GREATER THAN 15.
Eliminate B.

The correct answer is D.