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 100 figures in that book?

Which one of the following is correct in respect of the above Statements and the Question?

Correct Option: S1 and S2 together are not sufficient to answer the Question.

Let us analyze the given statements step-by-step to determine if we can answer the question: "Are there more than 100 figures in that book?"

Statement 1 (S1): There are not more than two figures on any page of a 51-page book.
This means each page contains at most 2 figures. That is, the number of figures on any single page can be 0, 1, or 2.
From S1 alone, the total number of figures in the 51-page book could range from 0 (if every page has 0 figures) up to a maximum of:

$51\times 2=102$

Since the total number of figures could be any value from 0 to 102, S1 alone is not sufficient to tell whether the total is strictly greater than 100.

Statement 2 (S2): There is at least one figure on every page.
This means each of the 51 pages contains 1 or more figures.
From S2 alone, the minimum total number of figures is:

$51\times 1=51$

However, there is no upper limit specified in S2. The total number of figures could be 51, 60, 100, or even 200. Thus, S2 alone is not sufficient to answer the question.

Combining both Statements (S1 and S2):
From S2, every page has at least 1 figure.
From S1, every page has at most 2 figures.
Therefore, the number of figures on each page is either 1 or 2.

Let us find the minimum and maximum possible total number of figures in the 51-page book using both statements:

1. Minimum possible figures: If every page has 1 figure, the total number of figures is:

$51\times 1=51$

In this case, 51 is not more than 100 (Answer: No).

2. Maximum possible figures: If every page has 2 figures, the total number of figures is:

$51\times 2=102$

In this case, 102 is more than 100 (Answer: Yes).

3. Intermediate possibilities: If 50 pages have 2 figures each and 1 page has 1 figure, the total is 101 (Answer: Yes). If 49 pages have 2 figures each and 2 pages have 1 figure, the total is 100 (Answer: No).

Since the total number of figures can be 100 or less (e.g., 51, 100) or strictly more than 100 (e.g., 101, 102), we cannot give a definite "Yes" or "No" answer even when combining both S1 and S2.

Hence, S1 and S2 together are not sufficient to answer the Question.