What is the minimum number of different numerals needed to ?ll a 3×3 square matrix?
Correct Answer: 4
Solution and Explanation
Given that n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral.
Also, two cells are called adjacent if they touch each other horizontally, vertically or diagonally. As per the given definition, in the following matrix, the following are the cases of adjacent cells.
As per the information, we’ve the following diagram for a 3 x 3 matrix to have minimum number of numerals.
So, we require 4 elements to have all different numerals. Ans : 4
What is the minimum number of different numerals needed to ?ll a 5×5 square matrix?
Correct Answer: 4
Solution and Explanation
Given that n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral.
Also, two cells are called adjacent if they touch each other horizontally, vertically or diagonally. As per the given definition, in the following matrix, the following are the cases of adjacent cells.
As per the information, we’ve the following diagram for a 5 x 5 matrix to have minimum number of numerals.
So, we require 4 elements to have all different numerals.Ans : 4
Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to ?ll a 5×5 matrix?
- 16
- 4
- 25
- 9
The Correct Option is B
Solution and Explanation
The correct answer is (B):
Given that n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral.
Also, two cells are called adjacent if they touch each other horizontally, vertically or diagonally. As per the given definition, in the following matrix, the following are the cases of adjacent cells.
Even if one mistake is allowed, then also there won’t be any change in the solution given above. Ans : 4
Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5×5 square matrix?
- 9
- 16
- 4
- 25
The Correct Option is A
Solution and Explanation
The correct answer is (A):
Given that n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral.
Also, two cells are called adjacent if they touch each other horizontally, vertically or diagonally. As per the given definition, in the following matrix, the following are the cases of adjacent cells.
Given that all the cells adjacent to any particular cell must have different numerals, which is satisfied only when there are at least 9 numerals. Ans : 9
Top Questions on Data Analysis
- The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs.
The following additional information is known.
The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.
The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.
- The two plots below give the following information about six firms A, B, C, D, E, and F for 2019 and 2023.
PAT: The firm’s profits after taxes in Rs. crores,
ES: The firm’s employee strength, that is the number of employees in the firm, and PRD: The percentage of the firm’s PAT that they spend on Research and Development (R&D).
In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the two years.
- The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row. - Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's. - The chart below shows the price data for seven shares – A, B, C, D, E, F, and G as a candlestick plot for a particular day. The vertical axis shows the price of the share in rupees. A share whose closing price (price at the end of the day) is more than its opening price (price at the start of the day) is called a bullish share; otherwise, it is called a bearish share. All bullish and bearish shares are shown in green and red colour respectively.
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Time and Work
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Time and Work
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems