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.
What is the row number which has the least sum of numbers placed in that row?
Correct Answer: 4
Solution and Explanation
To determine the row with the least sum of numbers, we need to carefully analyze the
placement of the numbers in the grid based on the given conditions.
(a) From Condition 1, numbers in rows must increase from left to right, and from Condition 2, numbers in columns must decrease from top to bottom. This restricts the placement of higher numbers like 9 and 10.
(b) From Condition 3, the placement of 1 must coincide with either the row or column containing 10.
(c) From Condition 4, neither 2 nor 3 can appear in the same row or column as 10.
(d) Condition 5 eliminates 7 and 8 from the row or column containing 9.
(e) Condition 6 requires 4 and 6 to be in the same row.
Based on these constraints, we evaluate each row’s possible sum. After placing the num-
bers, the row with the least sum is Row 4.
Thus, the correct answer is: 4 .
Which of the following statements MUST be true?
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
- Only II
- Both I and II
- Neither I nor II
- Only I
The Correct Option is B
Solution and Explanation
Using the given conditions, we can determine the following placements:
- From Condition 1, numbers in rows must increase from left to right.
- From Condition 2, numbers in columns must decrease from top to bottom.
- Condition 3 ensures that 1 is in the same row or column as 10. If 10 is in Row 1, then 1 must be in Row 1.
- Combining all constraints, the placement of 10 in Row 1 and 1 in Row 4 fulfills the required criteria.
Thus, both statements (I) and (II) are true.
Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
- Only II
- Neither I nor II
- Only I
- Both I and II
The Correct Option is B
Solution and Explanation
Based on the conditions:
- From Condition 3, 2 cannot be in the same row or column as 10. Thus, it cannot
necessarily occupy Column 2. - From Condition 4, 3 is not required to be placed in Column 3. Its placement depends
on other conditions that are not fulfilled here.
As a result, neither statement I nor II must be true, making the correct option 2. Neither I nor II.
For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
Correct Answer: 2
Solution and Explanation
Based on the given constraints, we can deduce the following:
(a) 1 and 10:
• Must be in the same row or column.
• Due to increasing rows and decreasing columns, they must be placed in opposite corners.
• Possible placements:
– 1 in Row 1, Column 1 and 10 in Row 4, Column 1.
– 1 in Row 4, Column 4 and 10 in Row 1, Column 4.
(b) 4 and 6:
• Must be in the same row.
• Cannot be in Row 1 or Row 4 (due to 1 and 10).
• So, they must be in either Row 2 or Row 3.
(c) 2, 3, 7, and 8:
• Their placements are restricted by the placements of 1, 10, 4, and 6.
(d) Uncertain Slots:
• Due to these constraints, we cannot definitively determine the placement of num-
bers in the following two slots:
– The slot in Row 4, Column 2 or Column 3: This slot cannot be filled with 1, 2, 3, 4, 6, 7, 8, or 10.
– The other slot in Row 4: This slot also cannot be filled with 1, 2, 3, 4, 6, 7, 8, or 10.
Therefore, the answer to the question ”For how many slots in the grid, placement of
numbers CANNOT be determined with certainty?” is 2.
| Column 1 | Column 2 | Column 3 | Column 4 |
|---|---|---|---|
| Row 1 | 1 | 2 | 3 |
| Row 2 | 4 | 5 | 6 |
| Row 3 | 7 | 8 | 9 |
| Row 4 | 10 |
Note: Other valid configurations may exist, but the number of uncertain slots remains
the same.
What is the sum of the numbers placed in Column 4?
Correct Answer: 20
Solution and Explanation
Based on the given constraints, we can deduce the following:
(a) 1 and 10:
• Must be in the same row or column.
• Due to increasing rows and decreasing columns, they must be placed in opposite corners.
• Possible placements:
– 1 in Row 1, Column 1 and 10 in Row 4, Column 1.
– 1 in Row 4, Column 4 and 10 in Row 1, Column 4.
(b) 4 and 6:
• Must be in the same row.
• Cannot be in Row 1 or Row 4 (due to 1 and 10).
• So, they must be in either Row 2 or Row 3.
(c) 2, 3, 7, and 8:
• Their placements are restricted by the placements of 1, 10, 4, and 6.
Determining the Sum of Column 4:
Considering the constraints and the possible placements, we can deduce that:
- Column 4 must contain the numbers 1, 9, and 10.
Therefore, the sum of the numbers in Column 4 is:
1 + 9 + 10 = 20
Thus, the final answer is 20.
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.
- 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.
- The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.
The following additional facts are known about the schedule of games in the tournament.
1. Each team played against a team from the other group in Round 8.
2. In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match ups were identical.
3. Team 4 played Team 6 in both Round 1 and Round 2.
4. Team 1 played Team 5 ONLY once and that was in Round 2.
5. Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
6. In Round 8, Team 3 played Team 6, while Team 2 played Team 5.
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