Comprehension
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.
Question: 1
Which of the following can be true?
Which of the following can be true?
Show Hint
Look for geometric progressions or arithmetic sequences in questions involving marks and totals, as they often define relationships between different values.
Updated On: Sep 16, 2025
- Sumana scored 3 marks in the second test
- Sumana scored 4 marks in the eighth test
- Ravi scored 4 marks in the third test
- Sumana scored 2 marks in the first test
- Ravi scored 0 marks in the fifth test
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The Correct Option is D
Solution and Explanation
Step 1: Analyze the problem conditions.
- Ravi and Sumana scored the same marks from the second to eighth tests. - Sumana's marks from the fifth test onwards are the same as Ravi's marks. - The total marks of Ravi for the first three tests are the same as Sumana’s total marks in the first two tests. - Sumana’s marks in the first test, total marks of the first two tests, and total marks of the eight tests form a geometric progression.
Step 2: Find the true condition.
Based on the given information, the condition (D) that "Sumana scored 2 marks in the first test" is consistent with the progression and matches the conditions.
Final Answer: \[ \boxed{\text{(D) Sumana scored 2 marks in the first test}} \]
- Ravi and Sumana scored the same marks from the second to eighth tests. - Sumana's marks from the fifth test onwards are the same as Ravi's marks. - The total marks of Ravi for the first three tests are the same as Sumana’s total marks in the first two tests. - Sumana’s marks in the first test, total marks of the first two tests, and total marks of the eight tests form a geometric progression.
Step 2: Find the true condition.
Based on the given information, the condition (D) that "Sumana scored 2 marks in the first test" is consistent with the progression and matches the conditions.
Final Answer: \[ \boxed{\text{(D) Sumana scored 2 marks in the first test}} \]
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Question: 2
If Ravi scored 4 marks in the first test, how many marks did Sumana score in the third test?
If Ravi scored 4 marks in the first test, how many marks did Sumana score in the third test?
Show Hint
In problems involving geometric progressions, always use the first term and the common ratio to find unknown terms.
Updated On: Sep 16, 2025
- 4
- 3
- 1
- 0
- 2
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The Correct Option is B
Solution and Explanation
Step 1: Analyze the data.
Since Ravi and Sumana scored the same marks in the tests from the second test onwards, we know Sumana scored 4 marks in the first and second tests.
Step 2: Use the geometric progression rule.
Sumana’s marks are in a geometric progression with the first term being 4 marks. Based on this progression, Sumana's third test marks are 3.
Final Answer: \[ \boxed{\text{(B) 3}} \]
Since Ravi and Sumana scored the same marks in the tests from the second test onwards, we know Sumana scored 4 marks in the first and second tests.
Step 2: Use the geometric progression rule.
Sumana’s marks are in a geometric progression with the first term being 4 marks. Based on this progression, Sumana's third test marks are 3.
Final Answer: \[ \boxed{\text{(B) 3}} \]
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Question: 3
If Ravi scored 1 mark in the second test, what is the maximum possible value of Sumana’s total marks in all the eight tests together?
If Ravi scored 1 mark in the second test, what is the maximum possible value of Sumana’s total marks in all the eight tests together?
Show Hint
When dealing with sequences or progressions, check if the information provided is sufficient to calculate the total value, or if some values remain undetermined.
Updated On: Sep 16, 2025
- 10
- 9
- 12
- Cannot be uniquely determined from the given information
- 8
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The Correct Option is D
Solution and Explanation
Step 1: Understand the conditions.
We know that the total marks of the eight tests for Sumana and Ravi form a geometric progression, and there are conditions governing their scores in different tests.
Step 2: Analyze the maximum total marks.
Since the exact values of Sumana's scores in all tests are not fully determined (due to the undefined values and geometric progression), we cannot uniquely determine her total marks.
Final Answer: \[ \boxed{\text{(D) Cannot be uniquely determined from the given information}} \]
We know that the total marks of the eight tests for Sumana and Ravi form a geometric progression, and there are conditions governing their scores in different tests.
Step 2: Analyze the maximum total marks.
Since the exact values of Sumana's scores in all tests are not fully determined (due to the undefined values and geometric progression), we cannot uniquely determine her total marks.
Final Answer: \[ \boxed{\text{(D) Cannot be uniquely determined from the given information}} \]
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