# CAT Quantitative Aptitude Questions | CAT Number Theory - Sum of first N natural numbers

###### CAT Questions | Number Theory | Sum of first N numbers
CAT Questions

The question is about Sum of first N natural numbers. Application of sum of first N numbers. We need to do trial and error to arrive at the answer. Dealing with digits and base system of a number is a vital component in CAT Number Theory. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 2: A page is torn from a novel. The sum of the remaining page numbers is 10000. What are 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

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##### Method of solving this CAT Question from Number Theory - Digits: Number Theory questions make us go from rigour to trial-and-error alternately. This is one such question.

$$frac{n$n+1$}{2}$ should be nearby 10,000, so n$n + 1) is somewhere near 20,000.
So n should be around √(20000) about 141.
Try 142
142 * 143 = 10153
141 * 142 = 10011
So, the missing pages are either 76 and 77 or 5 and 6.

The question is "What are the two page-numbers on the torn page of this novel?"

##### Hence the answer is "None of these"

Choice D is the correct answer.

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