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by sanju09 » Mon Feb 22, 2010 2:18 am
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
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by ajith » Mon Feb 22, 2010 3:13 am
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]
Last edited by ajith on Mon Feb 22, 2010 4:25 am, edited 5 times in total.
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by sanju09 » Mon Feb 22, 2010 3:23 am
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?
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by ajith » Mon Feb 22, 2010 3:38 am
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!
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by sanju09 » Mon Feb 22, 2010 3:47 am
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!
The mind is everything. What you think you become. -Lord Buddha



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by ajith » Mon Feb 22, 2010 4:24 am
sanju09 wrote: Characters changed yet character remains!
Edited again!

I am so happy that they have objective type questions in GMAT
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by sanju09 » Mon Feb 22, 2010 4:38 am
ajith wrote:
sanju09 wrote: Characters changed yet character remains!
Edited again!

I am so happy that they have objective type questions in GMAT
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by ajith » Mon Feb 22, 2010 4:41 am
sanju09 wrote: The titanic cost of pretty few things is never minded, HAPPINESS is one of these
Ahem! Let us not digress!
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