# CAT Practice : Number System

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Number Theory questions make us go from rigour to trial-and-error alternately. This is one such question.

## Sum of first n natural numbers

Q.2: A page is torn from a novel. The sum of the remaining page numbers is 10000. What is the sum of the two page-numbers on the torn page of this novel?
1. 77 and 78
2. 33 and 34
3. 8 and 9
4. None of these

Choice D. None of these

## Detailed Solution

n (n + 1) / 2
should be nearby 10,000, so n (n + 1) is somewhere near 20,000. So n should be around $\sqrt {20000}$ about 141.

Try 142
142 * 143 = 10153
141 * 142 = 10011
So, the missing pages are either 76 and 77 or 5 and 6.

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