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A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

  • A.54
  • B.65
  • C.66
  • D.76

Answer: D

The house number is 76.

Each statement is an 'if ... then' rule, so a number passes a rule automatically when the 'if' part is false. Test the options:

  • 76: not a multiple of 3, so rule i does not apply; a multiple of 4, so rule ii does not apply; not a multiple of 6, so rule iii requires 70 to 79, and 76 is. All three hold.
  • 54: not a multiple of 4, so rule ii demands 60 to 69. It fails.
  • 65: not a multiple of 6, so rule iii demands 70 to 79. It fails.
  • 66: a multiple of 3, so rule i demands 50 to 59. It fails.

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