What is the sum of the cubes of the first ten positive integers?

Hi All,

The answer choices to this question are "spread out" enough that we can avoid most of the "math" involved and get to the correct answer. We also don't need any special math knowledge or formulas beyond basic multiplication and some estimation.

We're asked for the sum of the CUBES of the first 10 positive integers.

First off, the GMAT would NEVER ask us to physically add up those 10 numbers, so there has to be another way to get to the solution. Let's do a little work and use the patterns in the math...

1^3 = 1
10^3 = 1,000

Since we're adding up 10 cubes, we know that the sum will be GREATER than 1,001 and since 10^3 is the biggest (and the other 9 cubes are SMALLER than 10^3), the sum MUST be LESS than 10,000. With this deduction, we can eliminate Answer A (1000), Answer D (10,000), and Answer E (1,000,000).

Between Answers B and C, we just have to do a little more work....

50^2 = 2500, so....
45^2 is LESS than 2500
55^2 is GREATER than 2500

9^3 = 81(9) = about 700
8^3 = 64(8) = about 500

Considering what we know about 10^3, we're already at 2200+, with 6 more cubes to go. This will certainly end up summing to a total that is GREATER than 2500. Eliminate Answer B.

Final Answer:

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