Latest Others Aptitude Question SOLUTION: From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

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(#M40003576) OTHERS question Missing pages Keep an EYE

From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808.
Which pages are missing?

Asked In Others Vasu (12 years ago)

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Dr.Dipin Singh  (12 years ago)

Let the number of missing pages be n and the first missing page number is p+1.
Then the pages p+1 up to and including p+n are missing,
sum of numbers on missing pages =
n(((p+1)+(p+n))/2)=9808

n*(2*p+n+1)= 32*613
One of the two terms n and 2*p+n+1 must be odd, and the other one must be even. Also the term n must be smaller than the term 2*p+n+1.
so there are only two possible cases:
n=1 and (2*p+n+1)=32*613, so n=1 and p=9807, so only page 9807+1 = 9808 is missing
which is not possible as at least 2 pages are counted when a leaf is missing.
other chance is
n=32 and 2*p+n+1=613, so n=32 and p=290, so the pages 291 up to and including 322 are missing.
hence the pages 291 up to 322 (including 322) are missing.

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Dr.Dipin Singh  (12 years ago)

number of missing pages = 32
pages from 291 to 322 are missing.

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Vinay  (12 years ago)

dipin can u plz explain ...how?
or any body who knw anser plz give explaintn

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