Project ForgeA 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?
- A54
- B65
- C66
- 76
Explanation
Test each candidate for contradictions with all three conditionals: 54 is a multiple of 3 (satisfies i, is in 50-59) but is NOT a multiple of 4, so (ii) requires it to be 60-69 — contradiction. 65 is not a multiple of 3 (i vacuous) and not a multiple of 4, so (ii) requires 60-69 (65 qualifies), but 65 is also not a multiple of 6, so (iii) requires 70-79 — contradiction. 66 is a multiple of 3, so (i) requires 50-59, but 66 isn't in that range — contradiction. 76 is not a multiple of 3 (i vacuous), IS a multiple of 4 (ii vacuous), and is NOT a multiple of 6, so (iii) requires 70-79, and 76 satisfies this with no contradictions.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.