GATE ME 2018 Set 1 — Question 6
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General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
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Question
For integers and , what would be the minimum and maximum values respectively of if ?
Correct answer
(A) -3 and 3
Solution
Given the equation:Using the property of logarithms :Taking the antilogarithm (base 10):Since and are integers, their absolute values and must also be integers. The only positive integer whose product is 1 is 1 itself. Therefore:This implies that each variable can be either or :Now, we find the possible values for the sum :
- Maximum value:
- Minimum value:
- Other possible values: and
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