Subjects quantitative reasoning

Diamond Sum

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Diamond Sum


1. Problem: Given the square value 150 and diamond cells 100 (top), 150 (left), 50 (right), 150 (bottom), determine if the values add correctly. Step 1: The diamond cells represent numbers around the square for addition and subtraction reasoning. Step 2: Check consistency: sum of two opposite diamonds should equal the square. Step 3: Check top and bottom: 100 + 150 = 250; this is not equal to the square 150. Step 4: Check left and right: 150 + 50 = 200; this is not equal to the square 150. Conclusion: Verify if the problem asks for missing values or validation; here, values donโ€™t sum to the square. 2. Problem: Square is 215; diamond cells top 150, left 200, bottom 150, right empty. Step 1: Sum of opposite diamonds equal square: top + bottom = 150 + 150 = 300; no match with 215. Step 2: Left + right = 200 + ? = 215; solve right = 215 - 200 = 15. Answer: Right diamond cell is 15. 3. Problem: Square empty; all diamond cells 75. Step 1: Calculate square value as sum of two opposite diamonds: 75 + 75 = 150. Answer: Square contains 150. 4. Problem: Square empty; diamond cells 125 (top), 125 (left), 150 (right), 200 (bottom). Step 1: Calculate square as sum of top and bottom: 125 + 200 = 325. Step 2: Check left and right sum: 125 + 150 = 275. Step 3: The square value is usually the average or consistent sum; likely square = 325. Answer: Square contains 325. 5. Problem: Square 75; diamond cells 50 (top), 25 (left), 50 (right), bottom empty. Step 1: Sum top and bottom = square; 50 + bottom = 75; bottom = 75 - 50 = 25. Step 2: Sum left and right = square; 25 + 50 = 75; consistent. Answer: Bottom diamond cell is 25. 6. Problem: Square 105; diamond cells 15 (top), empty (left), 75 (right), 75 (bottom). Step 1: Sum top and bottom = 15 + 75 = 90; should equal square 105, no. Step 2: Sum left and right = left + 75 = 105; left = 105 - 75 = 30. Answer: Left diamond cell is 30. Final answers: 1. Values inconsistent as given. 2. Right diamond = 15. 3. Square = 150. 4. Square = 325. 5. Bottom diamond = 25. 6. Left diamond = 30.