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?

The correct option is 76.

To identify the correct house number, we test the given options against the three statements. A conditional statement of the form "If A, then B" is logically true if the premise A is false (making the statement vacuously true), or if both the premise A and the conclusion B are true.

Let us verify why the number 76 satisfies all three statements:

Statement i: "If the house number is a multiple of 3, then it is a number from 50 to 59."
We check if 76 is a multiple of 3:
$76÷3=25.33$
Since 76 is not a multiple of 3, the premise is false. Thus, Statement i is true for 76.

Statement ii: "If the house number is NOT a multiple of 4, then it is a number from 60 to 69."
We check if 76 is a multiple of 4:
$76=4\times 19$
Since 76 is a multiple of 4, the premise ("is NOT a multiple of 4") is false. Thus, Statement ii is true for 76.

Statement iii: "If the house number is NOT a multiple of 6, then it is a number from 70 to 79."
We check if 76 is a multiple of 6:
$76÷6=12.67$
Since 76 is NOT a multiple of 6, the premise is true. The conclusion states that the number must be in the range of 70 to 79. Since 76 is indeed in this range, Statement iii is true for 76.

Since 76 is the only option that satisfies all three statements, it is the correct house number.