Four subjects, Physics, Chemistry, Mathematics, and Biology, are taught in four consecutive periods of one hour each, starting from 8:00 a.m. At what time is the Chemistry period scheduled? Consider the following statements: I. The Mathematics period ends at 10:00 a.m. and is immediately preceded by Biology. II. Physics is scheduled in the last period of the day. III. The Mathematics period is immediately followed by Chemistry. Which of the following options correctly describes which statement or statements are sufficient to answer the question?

Introduction / Context:
This data sufficiency question is about time scheduling of four subjects across four consecutive one hour periods starting at 8:00 a.m. The goal is to determine the time at which Chemistry is taught, based on different pieces of information about the order of subjects. The problem checks whether the learner can map statements to a time line and identify which combinations of statements uniquely fix the slot for Chemistry.

Given Data / Assumptions:

• There are four periods: 8 to 9 a.m., 9 to 10 a.m., 10 to 11 a.m., and 11 a.m. to 12 noon.
• The subjects are Physics, Chemistry, Mathematics, and Biology, each taught in exactly one period.
• Statement I says that Mathematics ends at 10:00 a.m. and is immediately preceded by Biology.
• Statement II says that Physics is taught in the last period.
• Statement III says that Mathematics is immediately followed by Chemistry.

Concept / Approach:
We represent each period by its time slot and try to place the subjects based on each statement. If a single statement gives a unique position for Chemistry, it is sufficient. If a statement leaves more than one possible arrangement, it is not sufficient. Next, we test pairs of statements to see whether the ambiguity is removed. Importantly, any combination that uniquely fixes the time of Chemistry is counted as sufficient.

Step-by-Step Solution:
Step 1: From statement I, Mathematics ends at 10:00 a.m. Therefore Mathematics is in the 9 to 10 a.m. period. Biology is immediately before Mathematics, so Biology is in the 8 to 9 a.m. period. The remaining two subjects, Physics and Chemistry, must then occupy 10 to 11 a.m. and 11 a.m. to 12 noon, but their order is not specified. Step 2: Using only statement I, Chemistry could be at 10 to 11 a.m. or at 11 a.m. to 12 noon. Since there are two possibilities, statement I alone is not sufficient. Step 3: From statement II alone, Physics is in the last period, that is, 11 a.m. to 12 noon. The positions of the other three subjects are not known, so Chemistry could be in any of the three earlier slots. Statement II alone is not sufficient. Step 4: From statement III alone, Mathematics is immediately followed by Chemistry, but there is no information regarding when Mathematics starts or ends. The pair Mathematics followed by Chemistry could occupy the first and second periods, the second and third periods, or the third and fourth periods. Hence statement III alone is also not sufficient. Step 5: Combine statements I and II. From I we know Biology at 8 to 9 a.m. and Mathematics at 9 to 10 a.m. From II we know Physics at 11 a.m. to 12 noon. This leaves only the 10 to 11 a.m. slot for Chemistry, so Chemistry is uniquely fixed at 10 to 11 a.m. Step 6: Combine statements I and III. Statement I fixes Mathematics at 9 to 10 a.m. and Biology at 8 to 9 a.m. Statement III says Mathematics is immediately followed by Chemistry, so Chemistry must be at 10 to 11 a.m. again. The time is now unique. Step 7: Combine statements II and III. From II we know Physics at 11 a.m. to 12 noon. From III we only know that Mathematics and Chemistry are adjacent in the order Mathematics, then Chemistry. However, these two subjects could occupy 8 to 9 and 9 to 10, or 9 to 10 and 10 to 11. Both patterns fit all the information, so Chemistry could be at 9 to 10 a.m. or at 10 to 11 a.m. This pair is not sufficient.

Verification / Alternative check:
A practical verification is to list all valid permutations under each combination of statements. For I alone, there are two permutations for the remaining subjects. For II alone, there are six permutations for the other three subjects. For III alone, there are three positions where the Mathematics Chemistry pair can be placed. For I with II and for I with III, only one valid overall permutation exists, and in each case Chemistry time is 10 to 11 a.m. For II with III, more than one permutation survives. This confirms the sufficiency pattern found earlier.

Why Other Options Are Wrong:
Option A claiming only I is sufficient is wrong because Chemistry can be placed in two different periods under statement I. Option B claims that either I or II alone is sufficient, which is incorrect because II alone clearly leaves three choices for Chemistry. Option C gives sufficiency to II alone, which is wrong for the same reason. The only correct description is that I combined with II, or I combined with III, is sufficient, which is option D.

Common Pitfalls:
Learners sometimes forget that the periods are fixed one hour blocks and misread phrases like immediately before or immediately after. Others may assume that last period must be 10 to 11 a.m., ignoring the fourth period. It is also easy to overlook that statement III does not specify any absolute time, only relative order. Careful mapping of each statement to the time line avoids these mistakes.

Final Answer:
The correct option is that statements I and II together or statements I and III together are sufficient to answer the question, which corresponds to option D.