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Consider three-digit numbers where the middle digit equals the sum of the other two digits, like 154 (1+4=5) and 275 (2+5=7).
How many three-digit numbers have this property?

Class 6Patterns in Whole NumbersWhole Numbers
  • A36
  • B42
  • C45
  • D54

Step-by-Step Solution

Let digits be a (1-9), b, c (0-9) with b = a + c and b <= 9. For each a from 1 to 9, c can range 0 to 9-a, giving (10-a) choices. Total = 9+8+7+6+5+4+3+2+1 = 45.
Answer: C) 45

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