A page is torn from a book. The sum of the remaining digits is 1977. What are the page numbers on pa

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28 Aug 2020 Arithmetic

A page is torn from a book. The sum of the remaining digits is 1977. 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 = 1977
⇒ n(n+1)/2 = 1977
n (n+1) = 3954
The square nearest to 3954 is 3969.This is the square of 63. Hence, we will take n= 63.
Therefore, sum of the pages= n(n+1)/2 = 63*64/2= 2016
Missing number = 2016-1977 =39.
Now, we have to think of 2 consecutive numbers whose sum is 39.
x+x+1=39 ⇒ ×= 19, x+1= 20

Correct Option: 7 Best Solution (2)

Bhargav   3 years AGO

number nearest to 1977 is 2016
and 2016=(62*64)/2
so 2016-1977=39
so 19,20 is the correct ans

Like? Yes | No (3)  

M4 Murali   3 years AGO

nearest possible sum of pages is 2016
2016-1977=39 20,19

Like? Yes | No (3)