All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?  Choose the correct choice from the following options.
A) 44
B) 45
C) 10
D) 12
E) 11
Explanation :   sum of n natural numbers = n (n+1)/2   Here, n( n + 1)/2 = 1000 - x (where x is the number that is added twice)   =&gt; n(n+1) &lt; 2000 - 2x   we need to find max value n can take . We know for a product of two numbers to be max the number should be closest. We need to find out the least number whose square is higher than 2000. For example, 452 = 2025.   So our number is somewhere near to 45. it can't be more than 45 as our required product is less than 2000.   44 * 45= 
<gadget id="calculator">44 * 45</gadget>
<output>1_980</output>
1980. So, we can have n= 44.   =&gt; n (n+1) = 44 * 45= 
<gadget id="calculator">44 * 45</gadget>
<output>1_980</output>
1980= 2000 - 2 * 10.   =&gt; x = 10.   Hence, we have 44 pages and page number 10 was added twice.   Answer : 10
<result>C</result>
All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?