A page is torn from a book. The sum of the remaining digits is 1097. What are the page numbers on pa

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30 Sep 2020 Arithmetic

A page is torn from a book. The sum of the remaining digits is 1097. What are the page numbers on page torn from this book?

OPtion

1) 17, 18
2) 18, 19
3) 10, 11
4) 11, 12
5) 13, 14
6) 12, 13
7) 19, 20
8) 14, 15
9) 15, 16
10) None of these

Solution

Let the total pages are 'n'. We have
1 + 2 + 3 + .........+n = 1097
⇒ n(n+1)/2 = 1096
n (n+1) = 2194
The square nearest to 2194 is 2209.This is the square of 47. Hence, we will take n= 63.
Therefore, sum of the pages= n(n+1)/2 = 47*48/2= 1128
Missing number = 1128-1097 =31.
Now, we have to think of 2 consecutive numbers whose sum is 31.
x+x+1=31 ⇒ ×= 15, x+1= 16

Correct Option: 9 Best Solution (0)