A house has a number which needs to be identified. The following three statements are given:
i. If the house number is...

Question

A house has a number which needs to be identified. The following three statements are given:
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

Accepted Answer

The house number is 76. Each statement is a conditional of the form 'if P then Q'. The contrapositive 'if not Q then not P' is equally valid. We must find a number that is consistent with all three statements. A number is 'consistent' with a statement if either the condition is false (so the statement is vacuously true) or both condition and conclusion are true.