## What is the value of $$27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2?$$

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### What is the value of $$27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2?$$

by M7MBA » Thu Jul 22, 2021 3:37 am

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A

B

C

D

E

## Global Stats

What is the value of $$27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2?$$

A. 6298
B. 6308
C. 6318
D. 6328
E. 6338

Source: GMAT Club Tests

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### Re: What is the value of $$27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2?$$

by regor60 » Wed Aug 25, 2021 11:21 am
Rewrite with 30 as the base:

(30-3)^2+(30-2)^2+(30-1)^2+30^2+ (30+1)^2+(30+2)^2+(30+3)^2.

Notice the second terms in each. Those will be squared, so will become 9,4,1,1,4,9. These total 28....

Notice these same second terms will be applied twice against 30 if they were multiplied out. Since there are the same terms both positive and negative, they will cancel out.

Now we are just left with seven sets of 30^2.

30^2=900. 7x900=6300.

6300+28=6328,D

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