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.

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

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 =  900So 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) = 900As 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.

number of scores possible = 251  15 + 1 ...= 237
Could anyone explain this last step ?