GATE ME 2018 Set 2 — Question 9
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
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?
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?
Correct answer
(D) 76
Solution
Let be the house number. We test each option against the three logical statements:(A) :
- Multiple of 3? Yes (). Range 50-59? Yes. (Statement i is True)
- Not a multiple of 4? Yes (). Range 60-69? No. (Statement ii is False)
- Multiple of 3? No. (Statement i is vacuously True)
- Not a multiple of 4? Yes. Range 60-69? Yes. (Statement ii is True)
- Not a multiple of 6? Yes. Range 70-79? No. (Statement iii is False)
- Multiple of 3? Yes. Range 50-59? No. (Statement i is False)
- Multiple of 3? No (). (Statement i is vacuously True)
- Not a multiple of 4? No (). (Statement ii is vacuously True)
- Not a multiple of 6? Yes (). Range 70-79? Yes. (Statement iii is True)
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