Comprehension
There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of
coins in each column is also the same.
Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.
i) The minimum among the numbers of coins in the three sacks in the box is 1.
ii) The median of the numbers of coins in the three sacks is 1.
iii) The maximum among the numbers of coins in the three sacks in the box is 9.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of
coins in each column is also the same.
Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.
i) The minimum among the numbers of coins in the three sacks in the box is 1.
ii) The median of the numbers of coins in the three sacks is 1.
iii) The maximum among the numbers of coins in the three sacks in the box is 9.
Question: 1
How many boxes have at least one sack containing 9 coins?
How many boxes have at least one sack containing 9 coins?
Updated On: Jul 21, 2025
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The Correct Option is C
Solution and Explanation
To determine the number of boxes with at least one sack containing 9 coins, we need to analyze the information given in the problem. We have two tables with 3x3 arrangements, totaling 9 boxes. Each box contains 3 sacks. Our goal is to identify how many of these boxes have at least one sack with exactly 9 coins. According to the conditions provided:
- The median for some boxes is given. For any box where the median is 9, there must be at least one sack with 9 coins. These boxes need to be identified from Table 1.
- In Table 2, if a box has the conditions specified with "**" markers, it implies two or more of the conditions are satisfied, including condition (iii), which confirms the presence of a sack with 9 coins.
By examining these points against the data:
- Boxes with median 9 from Table 1 automatically qualify.
- Boxes marked with ** in Table 2 should also be included in the count, as they satisfy two or more conditions, including the maximum of 9 coins in at least one sack.
Thus, logically combining these deductions, there are 5 boxes that meet the criteria of having at least one sack with 9 coins.
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