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?
Show Hint
- 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
The Correct Option is D
Solution and Explanation
- 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: \[ \boxed{\text{(D) Sumana scored 2 marks in the first test}} \]
If Ravi scored 4 marks in the first test, how many marks did Sumana score in the third test?
Show Hint
- 4
- 3
- 1
- 0
- 2
The Correct Option is B
Solution and Explanation
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: \[ \boxed{\text{(B) 3}} \]
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
- 10
- 9
- 12
- Cannot be uniquely determined from the given information
- 8
The Correct Option is D
Solution and Explanation
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: \[ \boxed{\text{(D) Cannot be uniquely determined from the given information}} \]
Top Questions on Logical and Analytical Reasoning Skills
The diagram below represents a road network connecting five towns, namely Meeren, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown in the diagram. The straight road that connects Meeren to Gulltown passes through Oldtown. Another straight road, running west to east, connecting Meeren to Winterfell, passes through Lannisport. Further, two straight roads, one from Lannisport to Oldtown and another from Winterfell to Gulltown, are perpendicular to the road joining Meeren to Winterfell, and run from south to north.
Consider a car always travelling at the maximum permissible speed, and always taking the shortest route. It takes 1 hour to reach Oldtown from Meeren, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown. (For this problem, always consider the shortest route in terms of distance.)
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Questions Asked in XAT exam
Match the following renowned Indian personalities with their respective awards.
Names Award 1. Shri Ratan Naval Tata A. Dadasaheb Phalke Award 2. Manmohan Singh B. Grammy Awards 3. Zakir Hussain C. Carnegie Medal of Philanthropy 4. Shyam Benegal D. World Statesman Award - XAT - 2025
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Match the following authors with their respective works.
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Sundaram Stores operated in a gated community, situated about 30 Kilometers away from the main town. The store owner Mr. Sundareswaran Pichaimuthu, or Sundaram as he was called by everyone, secured a space in the gated society through a competitive bidding process. The residents’ association, led by Mr. Thangamoorthy Selvaganapathy, selected Sundaram over three other bidders, based on his willingness to pay the highest rent. Desperate to augment his post-retirement income, Sundaram agreed to pay a very high rent, banking on the prospect of generating exceptional revenue from the gated community.
Sundaram was awarded the contract to establish the store, with provisions for a review every three years. Feeling elated during the meeting with the residents’ association to finalize the contract, he enthusiastically committed to offering a 15% discount on all groceries and stationary, cementing goodwill and reinforcing the partnership established through the contract. The association was delightedly taken aback by his generous assurance. Sundaram hoped to make up the difference through volume.
Although his sales were strong during the initial months, he soon realized that the SUV-owning residents of the gated community primarily made their purchases at large, branded retail chains in the main town. These stores offered deeper discounts, which he could not afford to compete with. However, gradually, Sundaram store became their go-to store for daily essentials and occasional urgent big purchases such as replacing a broken mixer-grinder.- XAT - 2025
- Data Arrangement