GATE CE 2025 Set 2 — Question 8
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
Consider a five-digit number that has distinct digits , and , and satisfies the following conditions:
If integers 1 through 5 are used to construct such a number, the value of is:
If integers 1 through 5 are used to construct such a number, the value of is:
Correct answer
(C) 3
Solution
From the given conditions, we can establish a chain of inequalities: .
Since the digits are distinct and chosen from , we have 4 digits in this chain.
If , then must be 5. But must also be , so would have to be 5, which violates the distinct digits rule.
If , then can be 4 or 5, and can be the other value (4 or 5). and must be smaller than , so they must be . Specifically, and to satisfy . This works perfectly: or .
If , there is only one digit (1) smaller than , so we cannot satisfy . Thus, must be 3.
Since the digits are distinct and chosen from , we have 4 digits in this chain.
If , then must be 5. But must also be , so would have to be 5, which violates the distinct digits rule.
If , then can be 4 or 5, and can be the other value (4 or 5). and must be smaller than , so they must be . Specifically, and to satisfy . This works perfectly: or .
If , there is only one digit (1) smaller than , so we cannot satisfy . Thus, must be 3.
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