IS the answer E?
Hi Advait08,
I too think the answer is E.
Given that,
Cubic boxes are stacked in square layers:
So each layer is a square.
The bottom of the layer has 81 boxes:
Then the bottom layer has 9 rows and each row has 9 boxes.
Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it:
The second layer has 8 rows and each row has 8 boxes.
So, similarly third layer has 7 rows and each row has 7 boxes.
So by this time we might have understood that, it is
81+64+49+36+25+16+9+4+1.
So next don’t add everything, just add the units digit,
It will end with 5. So only answer choice is E(285).
Alternatively,
We can use the formulae,
Sum of first “n” square terms:
= (n (n+1)(2n+1))/6
So here,
9^2 + 8^2 + 7^2 + 6^2 + 5^2 + …..+1^2
Using the above formulae,
= (9*10*19)/6
= 285.
So the answer is E.
Hope it is clear.