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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. If the house number is a multiple of 3, then it is a number from 50 to 59. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. 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 house has a number which needs to be identified. The following three statements are given that can help in identifying the house number. If the house number is a multiple of 3, then it is a number from 50 to 59. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. What is the house number? Correct Answer 76

  • Condition 1: If the house number is a multiple of 3, then it is a number from 50 to 59.
    • Possibilities: 51, 54, 57
    • But if one of these is the right answer, then it should be a multiple of 4 and 6 which is not the case here.
  • Condition 2: If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
    • Possibilities: 61, 63, 65, 66, 67, 69
    • But if one of these is the right answer, it should be multiple of six (i.e. 66) and not a multiple of 3 (but 66 is multiple of 3). So it is not a required sample space.
  • Condition 3: If the house number is NOT a multiple of 6, then it is a number from 70 to 79.
    • Possibilities: 70, 71, 73, 74, 75, 76, 77, 79
    • But if one of these is the right answer, it should be multiple of 4 (i.e. 76) and not a multiple of 3 (i.e. 70, 71, 73, 74, 76, 77, 79).

So 76 is the correct answer.

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