One page is torn from a booklet whose pages are numbered in the usual manner

One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers.

1. 5, 6
2. 7, 8
3. 9, 10
4. 11, 12

Answer: B

Explanation

This is a question of arithmetic progression. Let the number of pages in the book be n. Let the sum of the torn pages be s.

Sum of consecutive numbers from 1 to n = n(n+1)/2 = 195 + s

n(n+1) = 390 + 2s

As a page with two numbers was torn, so the value of n(n+1) must be more than 390.

The minimum possible value of n(n+1) over 390, such that n is an integer is got when n = 20

So, n(n+1) = 20 × 21 = 420

So, sum of 20 pages = n(n+1)/2 = (20 × 21)/2 = 210

Hence, sum of the two numbers on the torn page = 210 - 195 = 15

Only option B yields 15 as sum, i.e. 7 + 8 = 15

• Exam Year: 2020