How many pages of book X did Robert read on Sunday? Consider the following statements: I. Book X has 300 pages, and two thirds of the pages had been read by Robert before Sunday. II. Robert read the last 40 pages of the book on the morning of Monday.

Introduction / Context:
This data sufficiency problem is based on reading progress through a book. Robert reads a certain part of book X before Sunday, some part on Sunday, and some part again on Monday. The question asks how many pages he read on Sunday, and the statements provide information about the total pages and pages read at specific times. The focus is to judge whether the statements contain enough information to determine the Sunday reading.

Given Data / Assumptions:

• Book X has a total of 300 pages.
• Statement I: Two thirds of the book were read by Robert before Sunday.
• Statement II: Robert read the last 40 pages of the book on Monday morning.
• Pages are read in order, with no skipping and no rereading, and all counts are exact.

Concept / Approach:
Let the total pages be T, pages read before Sunday be B, pages read on Sunday be S, and pages read on Monday be M. Since Robert eventually finishes the book, B + S + M = T. Data sufficiency requires checking whether the statements fix S uniquely. If S remains undetermined with one statement but determined when both are combined, then both statements together are necessary.

Step-by-Step Solution:
Step 1: From statement I, two thirds of the book were read before Sunday. For a book of 300 pages, two thirds of 300 is 200 pages. Thus B = 200 pages read before Sunday. Step 2: Using statement I alone, we know that 100 pages remain to be read at the start of Sunday, but we do not know how many of those pages are read on Sunday and how many on Monday. Therefore statement I alone is not sufficient to determine S. Step 3: From statement II, Robert read the last 40 pages on Monday. This tells us M = 40. However, it does not give any information about how many pages were left at the end of Sunday, nor about total pages or the fraction read before Sunday. Hence statement II alone is also not sufficient. Step 4: Now combine statements I and II. We already know from I that B = 200 and T = 300, so there are 100 pages left after Saturday. From II we know M = 40 pages on Monday. Since Robert finishes the book, we must have B + S + M = T, so 200 + S + 40 = 300. Step 5: Solve for S. The equation 200 + S + 40 = 300 simplifies to 240 + S = 300. Therefore S = 300 minus 240 equals 60 pages. Thus Robert read exactly 60 pages on Sunday. Step 6: Because neither statement alone gives enough information but their combination does, both statements together are necessary to answer the question.

Verification / Alternative check:
As a check, consider how many distributions of Sunday and Monday pages are possible under each statement. Under statement I alone, any pair (S, M) satisfying S + M = 100 with S and M positive would work, so there are many possibilities. Under statement II alone, S could be any number at all, as long as the book ends with 40 pages on Monday. Only when we impose both B = 200 and M = 40, along with T = 300, do we get a single value for S. Therefore the necessity of both statements is confirmed.

Why Other Options Are Wrong:
Option A is incorrect because statement I alone leaves an entire range of possible values for S. Option B is incorrect because statement II alone does not mention total pages or pages read before Sunday. Option C is wrong because neither statement alone suffices. Option E, which says that even both statements together are not sufficient, contradicts the clear derivation of S = 60 pages. Only option D correctly recognises that both statements together are required and sufficient.

Common Pitfalls:
Learners may assume that if a certain fraction of the book has been read before Sunday and a specific number of pages is read on Monday, then Sunday reading can be guessed from proportion, without doing the exact calculation. Another mistake is to forget that the sum of all reading sessions must equal the total pages. Careful bookkeeping with variables and the equation B + S + M = T prevents these oversights.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.