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

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) + sqrt(k+1))/(sqrt(k) + sqrt(k+1)) = 1/(sqrt(k) + sqrt(k+1)) <1/(n+n) <1/2n [spoiler]A [/spoiler]

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] Won't the item in bold be zero?

sanju09 wrote: Won't the item in bold be zero? Copy paste errors - Fixed in the original post, thanks for pointing out, you know that logic was right!

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] Characters changed yet character remains!

sanju09 wrote: Characters changed yet character remains! Edited again! I am so happy that they have objective type questions in GMAT

ajith wrote:sanju09 wrote: Characters changed yet character remains! Edited again! I am so happy that they have objective type questions in GMAT The titanic cost of pretty few things is never minded, HAPPINESS is one of these