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Find how many numbers are lying between 9999 9 2 99999^{2} and 10000 0 2 100000^{2} .


The answer is 199998.

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4 solutions

Tushar Malik
Sep 12, 2014

Total numbers lying between n 2 n^{2} and [ n + 1 ] 2 [n+1]^2 is 2 times n. Therefore 99999 × 2 = 199998 99999 \times 2 = 199998 is the answer.

is it really a level 3 ques.?

Kushagra Sahni - 6 years, 8 months ago

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overrated!!

Parth Lohomi - 6 years, 8 months ago

Yes I also was surprised because it is not at all difficult.

Tushar Malik - 6 years, 8 months ago

Did it the same way! Good solution

Shashank Pulagam - 6 years, 8 months ago
Saket Sharma
Sep 14, 2014

Excluding the numbers, there are (1000000^2 - 99999^2) - 1 = [(1000000+99999) (1000000-99999)] - 1 = 199999 1 - 1 = 199998

Afreen Sheikh
Jan 22, 2015

no. in between can be find by

( 10000 0 2 9999 9 2 ) 1 (100000^{2} - 99999^{2})-1

( 100000 99999 ) ( 100000 + 99999 ) 1 (100000-99999)(100000+99999)-1

( 1 × 199999 ) 1 (1\times199999) -1

hence 199998...1 is subtracted in order to exclude one of the given no.

Chaitu Sakhare
Oct 11, 2014

the ans will be 100000^2 -99999^2 -1 =199999-1=199998

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