Problem Solving

sanju09 wrote:Square roots of two successive positive integers, each greater than n^2 (n ≠ 0), differ by m, then m is less than
(A) 1/ (2 n)
(B) 1/n
(C) 2/n
(D) 3/n
(E) 4/n

ajith wrote:

sanju09 wrote:Square roots of two successive positive integers, each greater than n^2 (n ≠ 0), differ by m, then m is less than
(A) 1/ (2 n)
(B) 1/n
(C) 2/n
(D) 3/n
(E) 4/n

let the successive integers be m and m+1

sqrt(m) >n

sqrt(m+1) - sqrt(m+1)

=(sqrt(m+1) - sqrt(m+1))*(sqrt(m+1) - sqrt(m+1))/(sqrt(m+1) + sqrt(m+1))
= 1/(sqrt(m+1) + sqrt(m+1))
<1/(n+n)
<1/2n

[spoiler]A
[/spoiler]

sanju09 wrote:
Won't the item in bold be zero?

ajith wrote:

sanju09 wrote:Square roots of two successive positive integers, each greater than n^2 (n ≠ 0), differ by m, then m is less than
(A) 1/ (2 n)
(B) 1/n
(C) 2/n
(D) 3/n
(E) 4/n

let the successive integers be k and k +1

sqrt(k) >n

m = sqrt(k+1) - sqrt(k)

=(sqrt(k+1) - sqrt(k))*(sqrt(k+1) + sqrt(k+1))/(sqrt(k+1) + sqrt(k+1))
= 1/(sqrt(k+1) + sqrt(k+1))
<1/(n+n)
<1/2n

[spoiler]A
[/spoiler]

sanju09 wrote: Characters changed yet character remains!

ajith wrote:

sanju09 wrote: Characters changed yet character remains!

Edited again!

I am so happy that they have objective type questions in GMAT

sanju09 wrote: The titanic cost of pretty few things is never minded, HAPPINESS is one of these