Correct option is A
Solution:
Step 1: Understanding the problem
A both-side printed book means each sheet has two pages: front (odd p) and back (p+1).
Sum of page numbers on one sheet = p + (p+1) = 2p + 1, which is always odd.
Step 2: Sum for 9 sheets
If we pick 9 sheets, total sum = sum of 9 odd numbers.
Sum of 9 odd numbers is odd, so total sum is always odd.
Step 3: Minimum possible sum
Smallest pages: sheets with pages (1,2), (3,4), ..., (17,18).
Their sums: 3, 7, 11, 15, 19, 23, 27, 31, 35.
Adding:
3+7=10, 10+11=21, 21+15=36, 36+19=55, 55+23=78, 78+27=105, 105+31=136, 136+35=171.
So minimum possible sum = 171.
Step 4: Checking options
9×(9+1)/2 = 45 → less than 171 → impossible.
"divisible by 3" → many odd numbers ≥171 divisible by 3 → possible.
179 ≥171 and odd → possible.
171 = minimum → possible.
Answer:
The sum can never be 45.
