QUESTION

CSAT

Medium

Maths

Prelims 2020

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.

Select an option to attempt

Explanation

This is a question involving arithmetic progression. Let the total number of pages in the book be nn.

The sum of consecutive numbers from 1 to nn is given by the formula: Sum= 2n(n+1)2\frac{2n(n+1)}{2} ​This sum is approximately 195. Thus, we have: n(n+1)390n(n+1) \approx 390 Since a page with two numbers was torn, the actual value of n(n+1)n(n+1) must be greater than 390. The smallest possible value of n(n+1)n(n+1) greater than 390, where nn is an integer, occurs when n=20n=20.

Therefore, n(n+1)=20×21=420n(n+1)=20 \times 21=420 The sum of the first 20 pages is: 20×212=210\frac{20 \times 21}{2} =210 The sum of the two numbers on the torn page is: 210195=15210-195=15 Only option B gives the sum of 15, i.e., 7+8=157+8=15.

Hence, option B is the correct answer.

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