Quant Boosters - Sibanand Pattnaik - Set 1
sibanand_pattnaik last edited by
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.
sumit agarwal last edited by zabeer
there is a bit confusion i have.
100 + a^3 = -900 (a = -10)
so how would the answer change here?
zabeer last edited by zabeer
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.
sumit agarwal last edited by
number of scores possible = 251 - 15 + 1 ...= 237
Could anyone explain this last step ?