Discussion
Find the missing number :
Two circles are each divided into four quarters, with a number in each quarter and one in the centre:
| Top left | Top right | Bottom left | Bottom right | Centre | |
|---|---|---|---|---|---|
| First circle | 10 | 11 | 6 | 9 | 56 |
| Second circle | 12 | 10 | 7 | 8 | ? |
Answer: B
The missing number is 64.
In the first circle, the product of the top two numbers minus the product of the bottom two gives the centre:
\[ \begin{aligned} 10 \times 11 - 6 \times 9 &= 110 - 54 = 56 \\ 12 \times 10 - 7 \times 8 &= 120 - 56 = 64 \end{aligned} \]
Applying the same rule to the second circle gives 64. Simple sums do not work for the first circle (10 + 11 + 6 + 9 = 36), so a sum-based rule cannot be the pattern, and 44, 60 and 54 do not follow from the product rule.
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