13 in43 in
12 in18 in
13 in | 43 in | |
12 in | 18 in | |
Verified Answer :
- Observe the difference between known elements in the columns, specifically in the first column where \(13 - 12 = 1\).
- Apply this consistent difference of \(1\) to the remaining columns to find the missing values.
- Calculate \(y\) from the second column: \(43 - 1 = 42\).
- Calculate \(x\) from the third column: \(18 + 1 = 19\).
- The missing values are \(x = 19\) and \(y = 42\).
Explanation
- Analyze the table and identify a pattern.
The provided table is a \(2 \times 3\) grid with four known values and two missing values. Let the table be represented as:
| \(13\) | \(43\) | \(x\) \) \(12\) | \(y\) | \(18\) \) |
We are looking for a consistent logical pattern to determine the values of \(x\) and \(y\). Examining the columns, we notice a clear relationship between the entries in the first column: \(13 - 12 = 1\). This suggests a pattern where each element in the first row is exactly \(1\) greater than the corresponding element in the second row.
- Calculate the missing values.
Based on the observation that the first row element is \(1\) greater than the corresponding second row element, we can set up the following equations for the other two columns:
- For the second column: \(43 - y = 1\). Solving for \(y\), we get \(y = 43 - 1 = 42\).
- For the third column: \(x - 18 = 1\). Solving for \(x\), we get \(x = 18 + 1 = 19\).
Thus, the missing values are \(x = 19\) and \(y = 42\).
- Verify the result.
We now verify the consistency of the pattern.
The table is:
| \(13\) | \(43\) | \(19\) \) \(12\) | \(42\) | \(18\) \) |
Calculating the difference for each column:
- Column 1: \(13 - 12 = 1\)
- Column 2: \(43 - 42 = 1\)
- Column 3: \(19 - 18 = 1\)
The pattern is perfectly consistent across all columns. The missing values are \(x = 19\) and \(y = 42\).
Examples
This type of logic is frequently used in spreadsheet software or data management systems where each row or column follows a specific transformation rule. For example, if you have a list of base prices in one column and a corresponding list of sales tax or discounted prices in another, you can easily identify missing entries by applying the consistent difference between the two columns, just as we did here to find the missing values in our table.