At what time did Sonali leave her home for the office? Consider the following statements: I. Sonali received a phone call at 9:15 a.m. while she was at home. II. The car of Sonali reached the office at 10:15 a.m., which was 45 minutes after she left her residence.

Introduction / Context:
This data sufficiency question deals with travel time between home and office. The time at which Sonali left her home needs to be determined. Two statements give information about a phone call she received at home and the time her car reached the office. The problem tests understanding of time interval calculations and the ability to decide which statements are sufficient on their own.

Given Data / Assumptions:

• Statement I: Sonali received a phone call at 9:15 a.m. while she was at home.
• Statement II: The car of Sonali reached the office at 10:15 a.m., and this was 45 minutes after she left her residence.
• Travel time from her home to the office for this trip is constant at 45 minutes as implied in statement II.
• Times are given in the same day and time zone, with no breaks in the journey.

Concept / Approach:
The second statement directly relates the arrival time at the office to the departure time from home using a fixed journey duration. If that duration and arrival are known, the departure time can be calculated by simple subtraction. The first statement, however, gives only a point in time when Sonali was still at home but does not link that moment to the departure time, so we must examine each statement separately and then together.

Step-by-Step Solution:
Step 1: Use statement II alone. The car reached the office at 10:15 a.m., forty five minutes after Sonali left home. Let the departure time from home be T. Then T plus 45 minutes equals 10:15 a.m. Step 2: Solve for T. Subtract 45 minutes from 10:15 a.m. Ten fifteen minus forty five minutes is 9:30 a.m. Therefore, Sonali left her residence at 9:30 a.m. Step 3: This calculation is unique and uses only information from statement II. Hence statement II alone is sufficient to answer the question. Step 4: Now examine statement I alone. Knowing that Sonali received a phone call at 9:15 a.m. while she was at home tells us that she had not yet left by that time. She could have left at 9:16 a.m., 9:30 a.m., or any other time after 9:15 a.m. No further constraint is provided, so her exact departure time cannot be determined from this statement alone. Step 5: Even if we combine both statements, statement II already provides the complete answer. Statement I does not change the derived departure time; it only confirms that she was indeed at home fifteen minutes before leaving, which is consistent with leaving at 9:30 a.m.

Verification / Alternative check:
To verify sufficiency of statement II, consider whether any other departure time could lead to arrival at 10:15 a.m. with a fixed travel time of 45 minutes. Any such journey must start exactly 45 minutes earlier, at 9:30 a.m. There is no alternative. Conversely, with statement I, there is no information about the travel duration or arrival time, so multiple departure times are possible. This confirms that II alone is sufficient and I alone is not.

Why Other Options Are Wrong:
Option A is wrong because it gives sufficiency to statement I, which does not fix a unique departure time. Option C claims that either statement alone is sufficient, which is incorrect since I alone is not enough. Option D suggests that both statements together are necessary, but this is not true because II alone already yields the exact answer. Option E, claiming that even both together are not sufficient, is clearly false since we obtain a precise time of 9:30 a.m. when using statement II.

Common Pitfalls:
A common mistake is to overvalue statement I simply because it mentions a time when Sonali is at home. Learners may wrongly assume that the call at 9:15 a.m. is very near departure, but the question does not say that the call occurred immediately before she left. Another error is to confuse the phrase after forty five minutes with some vague time window, when it actually denotes a fixed travel duration. Reading the timing relations carefully avoids such errors.

Final Answer:
The data in statement II alone are sufficient to answer the question, while statement I alone is not sufficient, so the correct option is B.