Two statements S1 and S2 are given below followed by a Question: S1: There are not more than two figures on any page of a 51-page book. S2: There is at least one figure on every page. Question: Are there more than 1oo figures in that book? Which one of the following is correct in respect of the above Statements and the Question?

The question asks if there are more than 100 figures in a 51-page book. We need to determine if the given statements (S1 and S2) are sufficient to answer this question definitively (with a clear 'Yes' or 'No').

1. Analyze Statement S1: "There are not more than two figures on any page of a 51-page book." This means each page can have 0, 1, or 2 figures.

   • Minimum possible figures in the book = 0 figures/page * 51 pages = 0 figures.
   • Maximum possible figures in the book = 2 figures/page * 51 pages = 102 figures. Since the total number of figures could be 0 (not more than 100) or 102 (more than 100), S1 alone is not sufficient to answer the question.

2. Analyze Statement S2: "There is at least one figure on every page." This means each page can have 1, 2, 3, or more figures (no upper limit specified by S2 alone).

   • Minimum possible figures in the book = 1 figure/page * 51 pages = 51 figures.
   • Maximum possible figures in the book = theoretically infinite (if S2 is considered alone without any upper bound). Since the total number of figures could be 51 (not more than 100) or, for example, 3 figures/page * 51 pages = 153 figures (which is more than 100), S2 alone is not sufficient to answer the question.

3. Analyze Statements S1 and S2 together:

   • From S1: Each page has 0, 1, or 2 figures.
   • From S2: Each page has 1 or more figures. Combining both, each page must have either 1 or 2 figures.
   • Minimum possible figures in the book = 1 figure/page * 51 pages = 51 figures.
   • Maximum possible figures in the book = 2 figures/page * 51 pages = 102 figures. The question is: "Are there more than 100 figures in that book?"
   • If the book has 51 figures, the answer is 'No'.
   • If the book has 102 figures, the answer is 'Yes'. Since the combined statements allow for scenarios where the answer is 'No' (e.g., 51 figures) and scenarios where the answer is 'Yes' (e.g., 102 figures), S1 and S2 together are not sufficient to provide a definitive 'Yes' or 'No' answer to the question.

Based on this analysis:

• A) is incorrect because S1 and S2 together are not sufficient.
• B) is incorrect because S1 alone is not sufficient.
• C) is correct because S1 and S2 together are not sufficient to answer the Question.
• D) is incorrect because S2 alone is not sufficient.

The final answer is C