Subjects quantitative reasoning

Number Cross Sums

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Number Cross Sums


1. **Stating the problem:** We have four number crosses, each with four numbers arranged around a center and a sum below a horizontal line. Two sums are missing. We want to find the pattern used to get the sums. 2. **Analyzing the first cross:** Numbers are 8 (top), 48 (left), 32 (right), 64 (bottom), and sum is 152. 3. **Check if sum is just addition:** $8 + 48 + 32 + 64 = 152$. 4. **Analyze the second cross:** Numbers are 1 (top), 81 (left), 9 (right), 729 (bottom), sum is 820. 5. **Check if sum is addition:** $1 + 81 + 9 + 729 = 820$. 6. **Conclusion from first two:** The sum below is the direct sum of the four numbers around the cross. 7. **Apply to third cross (empty sum):** Numbers 85 (top), 45 (left), 68 (right), 18 (bottom). Sum: $85 + 45 + 68 + 18 = 216$. 8. **Check the fourth cross:** Numbers 520 (top), 545 (left), 570 (right), sum 2164, bottom number is missing in description (assuming 529 as needed). 9. **Verify sum in fourth cross:** Sum $520 + 545 + 570 + 529 = 2164$. 10. **Summary:** The sums shown are the simple sum of the four numbers surrounding the cross. 11. **Final answers:** - Third cross sum: $216$ - Fourth cross bottom number inferred: $529$ Thus, the reasoning is that the sum represents the simple addition of the four numbers around the cross.