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All the page numbers in a book are added, beginning from page 1. However, a page number was added twice by mistake. If the sum obtained was 850, which page number must have been added twice?
- a)25
- b)30
- c)35
- d)40
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
All the page numbers in a book are added, beginning from page 1. Howev...
Let the total number of pages in the book be ‘n’.
Let page number ‘x’ be repeated.
⇒ x + n(n+1) /2 = 850
So, n(n+1)/2 ≤ 850
⇒ n2 + n ≤ 1700
The greatest possible value of n = 40.
Now, for n = 40, n(n+1)/2 = 40×41/2 = 820
So, x = 30.
Let page number ‘x’ be repeated.
⇒ x + n(n+1) /2 = 850
So, n(n+1)/2 ≤ 850
⇒ n2 + n ≤ 1700
The greatest possible value of n = 40.
Now, for n = 40, n(n+1)/2 = 40×41/2 = 820
So, x = 30.
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Community Answer
All the page numbers in a book are added, beginning from page 1. Howev...
Explanation:
Given:
- Sum of all page numbers from 1 to n = 850
- One page number was added twice by mistake
Approach:
- Let's find the sum of all page numbers from 1 to n using the formula n(n+1)/2
- Subtract 850 from this sum to find the duplicate page number
Calculation:
- Sum of all page numbers from 1 to n = n(n+1)/2
- n(n+1)/2 = 850
- n^2 + n = 1700
- n^2 + n - 1700 = 0
- (n - 40)(n + 41) = 0
- n = 40 or n = -41
Conclusion:
- Since page numbers cannot be negative, the duplicate page number is 40 (option 'B').
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All the page numbers in a book are added, beginning from page 1. However, a page number was added twice by mistake. If the sum obtained was 850, which page number must have been added twice?a)25b)30c)35d)40Correct answer is option 'B'. Can you explain this answer?
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