CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Inequalities

The question is from Log and Exponents. A question on possible maximum value. We need to maximize the value of a - b under the given conditions. With every extra hour you log in for this topic, it becomes exponentially simpler. CAT Logarithms and Exponents is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 5: \\frac{log_3{x-3}}{log_3{x-5}}\\) < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.

  1. 214
  2. 216
  3. 200
  4. 203

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Simple inequalities questions appear exponentially tougher when Logarithms are thrown in.

\\frac{log_3{x - 3}}{log_3{x - 5}}\\) < 0
log3x = y
=> \\frac{y - 3}{y - 5}\\) < 0
y ∈ (3, 5)
3 < log3x < 5
27 < x < 243
Therefore max ( a – b) will be when a = 242 and b = 28. Therefore, max(a – b) = 214.

The question is "find the maximum possible value of a – b."

Hence, the answer is "214".

Choice A is the correct answer.


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