# Quant Boosters - Sibanand Pattnaik - Set 1

• As X started the distribution part and took a 10 rupee note first and in the end also, he is able to take a 10 rupee note. That means Total amount, which needs to be a perfect square for n mangoes @ n rupees per mango, is odd multiple of 10 plus some more which is less than 10. That means ten's place digit of the perfect square is ODD. So certainly unit digit of perfect square is 6.

• @sibanand_pattnaik

hi,
there is a bit confusion i have.
100 + a^3 = -900 (a = -10)
so how would the answer change here?

• @sumit-agarwal

Concept : When a polynomial f(x) is divided by (x - a), remainder is f(a)

Here, f(x) = 100 + x^3
Remainder [f(x)/(10 + x)] = f(-10)
= 100 - 1000 = - 900

So we can write, 100 + x^3 = Q * (10 + x) - 900 ---- (eq 1)
Where Q is some integer (quotient)

Now it is said that f(x) is perfectly divisible by 10 + x.
Means, 100 + x^3 = K * (10 + x) --- (eq 2)
Where K is another integer.

From eq 1 and 2,
Q * (10 + x) - 900 = K * (10 + x)
(Q - K) (10 + x) - 900 = 0
(Q - K)(10 + x) = 900

As we are asked for maximum value of x, we will take (Q - K) as 1.
So (10 + x) = 900
x = 900 - 10 = 890.

Most of the steps here are detailed for the purpose of better understanding and should come intutively otherwise.

• @sibanand_pattnaik

number of scores possible = 251 - 15 + 1 ...= 237

Could anyone explain this last step ?

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