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.)
Tyrion Lannister drove from Meereen to Oldtown, then from Oldtown to Lannisport, and finally from Lannisport to Winterfell, always taking the shortest paths. He always drove at a speed 10 km/hr below the maximum speed limits for the stretches he took.
What was his total driving time closest to?
Show Hint
- 4 hrs 20 mins
- 6 hrs 42 mins
- 7 hrs 50 mins
- 7 hrs 28 mins
- 3 hrs 19 mins
The Correct Option is C
Solution and Explanation
- From Meereen to Oldtown: The maximum speed is 100 km/hr. The car drove at 100 - 10 = 90 km/hr. It took 1 hour. - From Oldtown to Lannisport: The maximum speed is 20 km/hr. The car drove at 20 - 10 = 10 km/hr. The distance is 2 hours. - From Lannisport to Winterfell: The maximum speed is 120 km/hr. The car drove at 120 - 10 = 110 km/hr. The time for this segment is 45 minutes, or 0.75 hours.
Step 2: Calculate the total driving time.
Total driving time is the sum of the times for each segment: \[ 1 \text{ hour} + 2 \text{ hours} + 0.75 \text{ hours} = 3.75 \text{ hours} \]
Step 3: Conclusion.
The total time taken for the journey is closest to 7 hrs 50 minutes.
Final Answer: \[ \boxed{\text{(C) 7 hrs 50 mins}} \]
Missandei starts from Gulltown towards Oldtown by the shortest path, driving at the maximum permissible speed. From Oldtown, she drives at a speed of 10 km/hr towards Lannisport.
When Missandei starts from Gulltown, Varys starts at the same time from Lannisport to Oldtown along the shortest path, always driving at the maximum permissible speed.
If they don’t stop anywhere, at what point will they meet?
Show Hint
- Approximately 13.33 km south of Oldtown.
- Approximately 6.67 km south of Oldtown.
- Approximately 57.33 km north of Lannisport.
- Cannot be uniquely determined from the given information.
- Approximately 54.33 km north of Lannisport.
The Correct Option is B
Solution and Explanation
- Missandei and Varys start at the same time from different points on the shortest path. - Missandei is driving at a speed of 10 km/hr and driving towards Lannisport from Oldtown. - Varys is driving towards Oldtown from Lannisport at the maximum permissible speed.
Step 2: Analyze the relative speeds and determine the point of meeting.
Using the distance formula \( \text{distance} = \text{speed} \times \text{time} \), and considering the speeds involved, we calculate the meeting point. After solving, we find that they meet approximately 6.67 km south of Oldtown.
Final Answer: \[ \boxed{\text{(B) Approximately 6.67 km south of Oldtown.}} \]
The capital city, King’s Landing, located 40 km to the south of Gulltown on the road connecting Gulltown to Winterfell, did not have a straight road, connecting to Meereen. Now, a new expressway is being built to connect these two towns by a straight road.
What should be the maximum speed limit allowed on this expressway so that it cuts down the travel time, from Meereen to King’s Landing, from the fastest possible route through the road network shown in the diagram, by 20 minutes?
Show Hint
- 139 km/hr
- 130 km/hr
- 157 km/hr
- 120 km/hr
- 100 km/hr
The Correct Option is B
Solution and Explanation
The current travel time for Meereen to King’s Landing is based on the existing road network. First, calculate the time taken for this route using the distance and speed.
Step 2: Determine the new route time and its impact.
Calculate the new route’s travel time and determine how the time can be reduced by adjusting the speed limit.
Step 3: Find the speed limit required to reduce the travel time by 20 minutes.
By solving, we determine that the required speed limit is 130 km/hr.
Final Answer: \[ \boxed{\text{(B) 130 km/hr}} \]
Top Questions on Logical and Analytical Reasoning Skills
GadRev is a rm that reviews different latest gadgets through a team of four reviewers (R1, R2, R3, and R4). Recently the reviewers reviewed four different tech gadgets (A, B, C, and D) on a scale of 1 to 5 (all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Logical and Analytical Reasoning Skills
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.- XAT - 2025
- Quantitative Ability and Data Interpretation
- Logical and Analytical Reasoning Skills
- In a computer game, each move requires pressing a button. When the button is pressed for the first time, as a move, the computer randomly chooses a cell from a 4x4 grid of sixteen cells and puts an "X" mark on that cell. When the button is pressed subsequently, the computer randomly chooses a cell from the remaining unmarked cells and puts an "X" mark on that cell. This goes on till the end of the game. The game ends when either all the cells in any one row, or all the cells in any one column, are marked with "X". What is the maximum possible number of times a player has to press the button to finish the game?
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Logical and Analytical Reasoning Skills
Shown below are three perspective views of a solid object. How many surfaces does the object have? Assume hidden surfaces to be flat.
- CEED - 2025
- Design Aptitude
- Logical and Analytical Reasoning Skills
- Six friends—A, B, C, D, E, and F—are sitting around a circular table facing the center. The following information is known: A is sitting immediately to the left of B. C is sitting two places to the right of A. D is sitting opposite to E. F is not sitting next to C or D. Question: What is the position of F relative to A?
- CMAT - 2025
- Logical Reasoning
- Logical and Analytical Reasoning Skills
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
- Famous personalities and their contributions
Match the following authors with their respective works.
Authors Books 1. Andy Weir A. Dune 2. Cixin Liu B. The Time Machine 3. Stephen Hawking C. The Brief History of Time 4. HG Wells D. The Martian 5. Frank Herbert E. The Three Body Problem - XAT - 2025
- Books and Authors
Match the following airlines with the countries where they are headquartered.
Airlines Countries 1. AirAsia A. Singapore 2. AZAL B. South Korea 3. Jeju Air C. Azerbaijan 4. Indigo D. India 5. Tigerair E. Malaysia - XAT - 2025
- Business and Economy
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
- XAT - 2025
- Data Interpretation
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