Math Problem Statement
Answer this question and give many sample questions with solutions similar to it
Which number will replace the question mark?
53 50 47
42 41 40
? 200 160
Options:
A. 206
B. 220
C. 103
D. 108
Solution
Let's analyze the given problem.
We have a 3x3 grid, and the first two rows are filled with numbers, while the third row contains two numbers and a question mark:
\hline 53 & 50 & 47 \\ \hline 42 & 41 & 40 \\ \hline ? & 200 & 160 \\ \hline \end{array}$$ We need to determine the number that replaces the question mark in the third row. ### Step-by-step analysis: - Let's observe the pattern by considering the columns: 1. In the first column: $$53, 42, ?$$ 2. In the second column: $$50, 41, 200$$ 3. In the third column: $$47, 40, 160$$ We notice that the numbers in the third row (containing $$?, 200, 160$$) are considerably larger than the corresponding values in the first and second rows. This hints at a multiplicative or additive pattern that links the rows. ### Checking the columns individually: - First column: $$53, 42, ?$$ - The difference between $$53$$ and $$42$$ is $$53 - 42 = 11$$. - Hence, $$? = 42 - 11 = 31$$. Now, the missing value is $$31$$. ### The correct answer is $$31$$, but this option does not appear in the list provided. However, the explanation holds in terms of the observed pattern in the data. Would you like further clarification or additional examples based on this pattern? ### Related sample questions with solutions: 1. **Question**: $$\begin{array}{|c|c|c|} \hline 45 & 42 & 39 \\ \hline 32 & 30 & 28 \\ \hline ? & 190 & 150 \\ \hline \end{array}$$ **Solution**: First column difference: $$45 - 32 = 13$$, so $$? = 32 - 13 = 19$$. 2. **Question**: $$\begin{array}{|c|c|c|} \hline 60 & 57 & 54 \\ \hline 48 & 46 & 44 \\ \hline ? & 300 & 260 \\ \hline \end{array}$$ **Solution**: First column difference: $$60 - 48 = 12$$, so $$? = 48 - 12 = 36$$. 3. **Question**: $$\begin{array}{|c|c|c|} \hline 80 & 75 & 70 \\ \hline 64 & 60 & 56 \\ \hline ? & 500 & 450 \\ \hline \end{array}$$ **Solution**: First column difference: $$80 - 64 = 16$$, so $$? = 64 - 16 = 48$$. 4. **Question**: $$\begin{array}{|c|c|c|} \hline 35 & 32 & 29 \\ \hline 26 & 24 & 22 \\ \hline ? & 150 & 120 \\ \hline \end{array}$$ **Solution**: First column difference: $$35 - 26 = 9$$, so $$? = 26 - 9 = 17$$. 5. **Question**: $$\begin{array}{|c|c|c|} \hline 90 & 85 & 80 \\ \hline 75 & 71 & 67 \\ \hline ? & 600 & 540 \\ \hline \end{array}$$ **Solution**: First column difference: $$90 - 75 = 15$$, so $$? = 75 - 15 = 60$$. ### Tip: When faced with missing values in a grid, always check for consistent differences (additive or subtractive patterns) between corresponding elements in the rows or columns.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Pattern recognition
Subtraction
Column analysis
Formulas
-
Theorems
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Suitable Grade Level
Grades 6-8