Subjects quantitative reasoning

Oval Missing Values

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Oval Missing Values


1. The problem involves identifying the missing numbers (☐) in two sets of concentric ovals based on given numerical patterns. 2. Let's analyze the patterns in the known ovals to find the relationship: Top-left oval numbers (clockwise): 12, 4, 48, 3, 16 - Notice that $12 \times 4 = 48$ and $3 \times 16 = 48$. - Thus, the product of opposite numbers equals 48. Top-right oval numbers (clockwise): 15, 14, 210, 21, 10 - Check products of opposites: - $15 \times 14 = 210$ - $21 \times 10 = 210$ - So, the opposite pairs multiply to 210. 3. Apply this reasoning to bottom-left oval (clockwise): 7, 6, ☐, 14, 3 - We assume the product of opposite numbers is constant. - Opposite pairs are (7, 6), (☐, 14), and (3) at center or side. With 5 numbers, and given pattern, the product is likely consistent. - $7 \times 6 = 42$ - $14 \times ? = 42$ so missing number $= \frac{42}{14} = 3$ - The missing number is $3$. 4. Bottom-right oval (clockwise): 27, ☐, 729, 81, 9 - Using the same logic, find the product of opposites: - $27 \times ? = ?$ - Check $81 \times 9 = 729$ - So, likely product of opposites is 729 - Missing number $= \frac{729}{27} = 27$ Final answers: - Bottom-left missing number: $3$ - Bottom-right missing number: $27$