Common Description:
In an 8-week course, a professor administered a test at the end of each week. Each of the eight tests was scored out of 4 marks, and a student could only receive a non-negative integer score.
Two students, Ravi and Sumana, took the eight tests.
In the first test, Ravi and Sumana scored the same marks. From the second to eighth tests, Ravi scored the exact same non-zero marks. Sumana scored the same marks as Ravi from the fifth test onwards. Ravi’s total marks in the first three tests was the same as Sumana’s total marks in the first two tests. Also, Sumana’s marks in the first test, total marks of the first two tests, and total marks of the eight tests are in a geometric progression.
Which of the following CAN be true?
B
Step-by-Step Solution
Key idea: Same setup as P1, but we do not fix . We must check all valid pairs to see which option CAN be true.
Step 1: From P1, we know and .
Step 2: Check Option A: . If , , which exceeds the max score of 4. False.
Step 3: Check Option B: . If and , . This is valid (). So B can be true.
Step 4: Check Option C: . But is non-zero. False.
Step 5: Check Option D: , not an integer. False.
Step 6: Check Option E: , invalid. False.
Answer: B