# How to solve this question type

What is the value of 382+392+402+412+422382+392+402+412+422 ?

A. 7950

B. 7990

C. 8010

D. 8050

E. 8070

From GMAT club

Sorry posted the wrong question. Its 38^2 +39^2 + 40^2+ 41^2+ 42^2

you can find from here

https://www.h4exammate.com/test-packages-details.php?qpc=38

Hello Shilpi,

Remember that (a^2 + b^2) = [(a+b)^2 + (a-b)^2]/2.

If we pair 42 and 38 i.e. a=42 and b=38, (a+b) = 80 and (a-b) = 4; hence, 42^2 + 38^2 = [(80)^2 + (4)^2]/2 = 3208.

Similarly, pairing 41 and 39 gives us a value of 3202 for 41^2 + 39^2.

And of course, 40^2 is 1600.

Adding the 3 values gives us 8010, which is indeed the value of the expression posted by you.

This method only requires you to know the squares of numbers ending with ZERO and of course, knowledge of basic algebraic identities.

Hope this helps.

Arvind BT