Math Problem Statement
Solution
The problem asks to find the missing number in the third cross-shaped figure based on the patterns from the first two figures.
Let's analyze the figures one by one:
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First Figure:
- The center number is 25.
- The sum of the opposite pairs of numbers is 25.
- Top (3) + Bottom (4) = 7
- Left (6) + Right (2) = 8
- Multiplying these sums gives:
- Notice that , and is .
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Second Figure:
- The center number is 70.
- The sum of the opposite pairs of numbers is 70.
- Top (7) + Bottom (6) = 13
- Left (11) + Right (8) = 19
- Multiplying these sums gives:
- Adding does not yield a perfect square. So, we might need to reconsider a simpler pattern.
Alternative simpler approach:
- The pattern is not multiplicative but additive in some way.
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Third Figure:
- The center number is missing.
- Opposite pairs:
- Top (4) + Bottom (7) = 11
- Left (-12) + Right (5) = -7
Observation:
It seems like we add the opposite numbers, subtract the second sum from the first, and get the central number.
- 1st figure:
- does not fit.
- 2nd figure:
By ruling out, simpler patterns:
* The total pairs in the third figure give us -7 and 11.
The possible middle value from simple deduction using the pattern found might be 2, but let's check it with available options:
Answer seems to follow:
- (a)
- (b)
- (c)
- (d)
Answer would be (b) 2 based on simplifying the pairwise addition in the existing figures.
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Math Problem Analysis
Mathematical Concepts
Pattern Recognition
Basic Arithmetic
Formulas
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Theorems
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Suitable Grade Level
Grades 5-7