Correct option is D
Given:
- 9 papers are printed on both sides → so each paper has 2 pages
- Therefore, total number of pages = 9 × 2 = 18 pages
- The question asks: Which total (sum) of page numbers can NEVER occur for any 9 such double-sided papers taken from a book?
Concept Used:
When pages are printed on both sides of a sheet, the two page numbers on each sheet are always consecutive odd and even numbers, specifically of the form:
- Sheet 1 → pages 1 and 2
- Sheet 2 → pages 3 and 4
- Sheet 3 → pages 5 and 6
- … and so on
So, each paper contributes a sum of:
- (1 + 2) = 3
- (3 + 4) = 7
- (5 + 6) = 11
- …
Each pair of consecutive numbers has a sum = odd + even = odd number
And if we add up the page numbers for 9 such papers, we are adding 9 odd numbers
Important Insight:
- The sum of odd numbers (odd count) is always odd
- So, the total sum of 18 pages (drawn from double-sided sheets) must always be the sum of 9 odd numbers, hence an odd number
Now Evaluate the Options:
Check parity (even or odd):
- 199 → odd → possible
- 219 → odd → possible
- 235 → odd → possible
- 256 → even → NOT possible
Because sum of 9 odd numbers can never be even, 256 can never be the sum of such page numbers.
Final Answer: (D) 256
