 # Can you tell me...

1. Chandan Baranwal
I was reading a book with page numbers from 1 to 100,suddenly I found some pages are torn off. The sum of
the numbers on the remaining pages is 4949. Can you tell me how many pages are torn off?[/B][/h]
2. user_000
Sir,

Although the data given is insufficient, but I can try. You can see whether logic is right OR it falters.

Actual sum = 1 + 2 + ... + 99 + 100
= 100 x [1 + 100] x 0.5
= 5050

But, as you mentioned, that after tearing off, net pages = 4949

Sum of those pages which were torn = 5050 - 4949 = 101
Since, this number is more than 100 (the max page limit); minimum no. of torn pages = 2

From the data you provided, it is clear that first and last pages are intact.
=> Let us assume that 2 and 99 numbered pages are torn off.

Sum of remaining = 1 + 3 + 4 + ... + 97 + 98 + 100
= 1 + 48 x 101 + 100 = 49 x 101 = 4949

But, 99 = 33 + 66

So, if page numbered 2, 33, 66 are torn off (i.e., 3 in number), then also, sum total remains 4949 only. Similarly, sum remains same if 2, 33, 55, 11 pages are torn (i.e., 4 pages).

Hence, minimum 2 pages are torn.

If you can provide some other details, we can evaluate exact number of torn off pages.

Hope this helps...
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