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Algebra
®µD®A's Avatar
®µD®A
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31 Aug 2008 14:27:10 IST
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For 10th graders(Interesting):
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A leaf is torn from a paperback novel. The sum of the numbers on the remaining pages is 15000.What are the page numbers on the torn leaf!


 


 


P.S: This is a real easy one and if not solved until night i will post the solution(Not sure whether that would be correct)


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Pankti Kansara's Avatar

Pankti Kansara
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31 Aug 2008 21:41:23 IST
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is the ans 501?


sry m nt a 10th grader bt stil can i pls noe d ans?
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®µD®A
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31 Aug 2008 21:44:39 IST
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Hey you have yo find both the pages.

A paper has 2 pages on either side.
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.
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Joined: 15 Jun 2008
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31 Aug 2008 21:46:04 IST
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Torn Pages  = 25,26
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®µD®A
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31 Aug 2008 22:02:26 IST
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yes the answer is correct post the solution
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Little_Master
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31 Aug 2008 22:58:43 IST
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Let the sum of missing page numbers = m


15000 + m = n/2 ( 2*1 + (n - 1) * 1 )


                  = n/2 ( 1 +  n )


30000 + 2m = n^2 + n


n^2 + n - (30000 + 2m) = 0


Discriminant = 1 + 4 (30000 + 2m)


                        = 1 + 120000 + 8m


                        = 120001 + 8m


This has to be a perfect square since page numbers are natural numbers.


Perfect square next to 120001 is 120409 (347 * 347).


So 8m = 120409 - 120001


             = 408


        m = 408 / 8 


             = 51


So missing leaf page numbers are (51 - 1)/2, (51 + 1)/2


That is  25, 26


rate me pls !!!!!!!
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Rahul Duggal's Avatar

Rahul Duggal
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31 Aug 2008 23:23:59 IST
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nice problem!!
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®µD®A
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31 Aug 2008 23:34:41 IST
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All answers are correct but 25,26 is the only solution as 112 and 113 a page does not exist having this number.
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GANESH BHAGWAT
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24 Oct 2011 21:51:07 IST
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100,101 CAN ALSO BE THE SOLUTION
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GANESH BHAGWAT
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24 Oct 2011 21:52:55 IST
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 I have a problem in this question 

I got page 100,101 and number of pages 173 

can't this be possible. this value fit in the eqation 
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