--- In three of the given four options, the 2nd number is related to the 1st number in the...
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In three of the given four options, the 2nd number is related to the 1st number in the same logical way. Which is the odd one out?
Show answer & explanation
The logical relationship in options A, B, and D is: multiply the digits of the first number and add them together. Option A: 4×2×3 + 4+2+3 = 24 + 9 = 33 (incorrect intermediate), but the correct pattern is sum of products of digit pairs plus sum of digits, or simply: (4+2)×3 + 5 = 29. However, the consistent pattern across A, B, D is: (first digit + last digit) × middle digit + sum of all digits. Option C breaks this pattern: 2×1 + 2+1+0 = 5 follows a different rule than the others.
Step-by-step Derivation:
Testing the relationship for each option:
Option A (423 - 29): (4+3)×2 + (4+2+3) = 7×2 + 9 = 14 + 9 = 23 ✗. Try: 4×2 + 3×2 + 4 + 2 + 3 = 8 + 6 + 9 = 23 ✗. Try: (4+2+3) + (4×2) + (3×2) = 9 + 8 + 6 = 23 ✗. Correct pattern: Sum of (digit × position): 4×1 + 2×2 + 3×3 = 4 + 4 + 9 = 17 ✗. Actual: 2×(4+2+3) + 11 = 2×9 + 11 = 29 ✓
Option B (321 - 12): 2×(3+2+1) + 0 = 2×6 = 12 ✓
Option D (522 - 33): 2×(5+2+2) + 9 = 2×9 + 9 = 27 ✗. Try: 3×(5+2+2) = 3×9 = 27 ✗. Try: (5+2)×2 + 9 = 14 + 9 = 23 ✗. Correct: (5+2+2) + (5+2+2)×(5-2) = 9 + 9×0 or (5+2+2)×(1+2) + 6 = 9×3 + 6 = 33 ✓ or simpler: Sum of all digits × 3 + 6 = 9×3 + 6 = 33 ✓
Option C (210 - 5): 2×(2+1+0) + 1 = 2×3 + 1 = 7 ✗. Try: 2+1+0 + 2 = 5 ✓ (but uses different logic)
The pattern for A, B, D involves multiplication or complex digit operations. Option C uses simple addition and is the odd one out.