gbatistoti wrote:
amanvermagmat wrote:
fameatop wrote:
First of all, two options(31,79) are very poorly framed & thus creating confusion. Anyways, the logic that the author wants to check is
No of books that can be read on any day = 2n+1 , where n is even integer.
2n+1 = even + odd = odd
So 2n+1 can never be even. Option C fits this bill.
Hence the answer.
Note- botanist can not read 31, 79 books as well. But i am assuming there is sth wrong with these two options.
Fame
Hi fameatop
there is nothing wrong with the options.. think of it this way: the total no of trees to be studied is n^2, divisor is (2n+1).. now the question asks which of the following CANNOT be the remainder? (13, 28, 17, 31, 79)... if we just divide n^2 by (2n+1) quotient will be (n/2) and remainder will be (-n/2)..
this remainder of (-n/2) can also be written as (2n + 1 - n/2) or (3n/2 + 1)... which means the remainder (or the no of trees on last day) will always be of the form (3n/2 + 1) where n is even (so 2 in denominator will be reduced/cancel out) which means this number will be of the form 3K + 1 where k is an integer... so whichever option does not satisfy this will be our answer... that is only one option, option C
(now i know some of you would be thinking 'how the hell is the quotient n/2 and remainder -n/2'... well that is a mathematical concept and i am not yet prepared to explain how it comes.... for you explanation by Bunuel is the best (anyday)..
Could someone explain how the remainder of (-n/2) can also be written as (2n + 1 - n/2) or (3n/2 +1) ? It is the only thing I got stuck in this explanation.
Thank you.
You asked this question long back - somehow i missed. I will try to explain now.
This is a concept of positive/negative remainders, which can be explained simply with an example. Lets say you divide 14 by 8, giving you a quotient of 1, and remainder of 6. That's because 14 = 8*1 + 6
Now interesting thing is this same remainder of '6' can also be said to be a remainder of '-2'. How you may ask? Thats because you can also write 14 as:
14 = 8*2 - 2 (I have increased the quotient by 1, from '1' earlier to '2' now)
14 can be written as a 8K + 6 (a multiple of 8 plus 6) and also be written as 8m - 2 (a multiple of 8 minus 2). Similarly if we divide 20 by 7, we can say the remainder is '-1' or we can say that the remainder is '6'. Because 20 = 7*3 - 1 or 20 = 7*2 + 6 (I have decreased the quotient by 1, from '3' earlier to '2' now)
By similar logic, when we divide n^2 by 2n+1 we can say remainder is '-n/2' because n^2 can be written as = (2n+1)*(n/2) - n/2
But we can also say that the remainder is '3n/2 + 1' because n^2 can also be written as = (2n+1)*(n/2 - 1) + (3n/2 + 1)
(I have just decreased the quotient by 1, from n/2 to n/2 - 1)