Identical blocks are stacked in rows to create a tower 24 rows tall. If the top row of the tower consists of four blocks

BTGmoderatorDC wrote: ↑

Sun Apr 24, 2022 5:07 pm

Identical blocks are stacked in rows to create a tower 24 rows tall. If the top row of the tower consists of four blocks, and each row below the top row consists of eight more blocks than the row directly above it, how many blocks are in the entire tower?

A. 2300
B. 2301
C. 2302
D. 2303
E. 2304


OA E

Source: Princeton Review

Number of blocks in row #1: 4
Number of blocks in row #2: 4 + 8
Number of blocks in row #3: 4 + 8 + 8
Number of blocks in row #4: 4 + 8 + 8 + 8
Number of blocks in row #5: 4 + 8 + 8 + 8 + 8
.
.
.
Number of blocks in row #24: 4 + 8 + 8 + 8 + 8 + 8 + 8.......

We want to find the sum of all of the above numbers.
When we add all of the 4's we get (24)(4)

Notice that (24)(4) = (12)(2)(4) = (12)(8), which means (24)(4) is divisible by 8

Since we are adding a bunch of 8's to (24)(4), we know that the final answer must be divisible by 8

When we check the answer choices, we see that only answer choice E is divisible by 8

Answer: E