An hour long test contains 60 problems. A student manages to solve 30 of these problems in 25 minutes. Based on this information, how many seconds on average does the student have available for solving each of the remaining problems in the time still left in the test?

Introduction / Context:

This aptitude question focuses on speed and time management in the context of an examination. It checks whether the student can correctly interpret the remaining time, convert minutes to seconds, and then distribute that time equally among the remaining unsolved questions. This type of calculation is common in competitive exams where candidates must decide how much time they can afford to spend on each question.

Given Data / Assumptions:

• Total duration of the test is 60 minutes.
• Total number of problems in the test is 60.
• The student solves 30 problems in the first 25 minutes.
• The remaining 30 problems must be solved in the remaining time of the test.
• We assume that the student uses all the remaining time for the remaining problems.

Concept / Approach:

The key idea is to calculate the time left after solving the first batch of problems and then divide this remaining time by the number of remaining problems. We must also convert minutes into seconds because the answer choices are given in seconds. The average time per problem is simply total remaining seconds divided by the number of remaining questions.

Step-by-Step Solution:

Verification / Alternative Check:

If the student spends exactly 70 seconds on each of the remaining 30 questions, total time used for them is 30 * 70 = 2100 seconds, which is equal to 35 minutes. Adding back the initial 25 minutes gives 25 + 35 = 60 minutes, which matches the full test duration, so the calculation is accurate.

Why Other Options Are Wrong:

Options like 50, 40, or 30 seconds would use less than the available time. That would sum to 1500, 1200, or 900 seconds respectively for the remaining questions, leaving unused time and not matching the distribution based on the given conditions. Only 70 seconds per question correctly uses all of the remaining 35 minutes.

Common Pitfalls:

Students sometimes forget to convert minutes into seconds or mistakenly divide total time (60 minutes) by total questions (60), which would ignore the fact that 25 minutes have already been spent. Another common error is to mix up solved and unsolved counts, dividing by 60 instead of 30. Carefully distinguishing between used time, remaining time, solved problems, and remaining problems avoids these mistakes.

Final Answer:

The average time available for each of the remaining problems is 70 seconds per problem.