There are not more than two figures on any page of a 51-page book

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?

1. Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
2. S1 alone is sufficient to answer the Question.
3. S1 and S2 together are not sufficient to answer the Question.
4. S2 alone is sufficient to answer the Question.

Answer: C

Explanation

As per statement 1, there are 2, 1 or 0 figures on each page. There are 51 pages in the book. So, maximum possible images in the book = 51 × 2 = 102. And the minimum possible images in the book = 0. So, statement 1 alone is not sufficient.

As per statement 2, there is 1, 2, 3, 4, ..., ∞ images on each page. But we do not know the number of pages in the book. So, statement 2 alone is not sufficient.

If we use the two statements together, then we know that there are 51 pages in the book. Every page must have 1 or 2 images. So, maximum possible images in the book = 51 × 2 = 102. And the minimum possible images in the book = 51 × 1 = 51. But we still cannot answer whether there are more than 100 figures in the book.

So, even S1 and S2 together are not sufficient to answer the question.

• Exam Year: 2020