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CAT 2001 — QA Question 23

Arithmetic ProgressionEasy

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?

Answer & solution

  • A

    44

  • B

    45

  • 10

  • D

    12

Solution

First we have to find the total number of pages in the book. For this we need to find the sum of the first few natural numbers, such that we reach to a number just short of 1000.

By trial and error, we can find that,

Sum of the first 44 natural numbers = =44(45)2 = 90

∵ 990 + 10 = 1000

∴ The page number added twice was 10.

Hence, option (c).

CAT 2001 QA Q23: All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added — Solution | TheCATExam