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

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

Explanatory Answer

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
\\frac{142 * 143}{2}\\) = 10153
\\frac{141 * 142}{2}\\) = 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.