Question Bank • QB_GA_QA_009 MCQ • 1 Mark

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

If $\log_{10}(x) + \log_{10}(x - 3) = 1$, the value of $x$ is:

Options:

  • (A) 5
  • (B) 2
  • (C) -2
  • (D) 10

Answer Key:

A

Step-by-Step Solution & Explanation

Using the logarithmic property $\log_{10}(a) + \log_{10}(b) = \log_{10}(ab)$: $\log_{10}[x(x - 3)] = 1 \implies x(x - 3) = 10^1 = 10$ $x^2 - 3x - 10 = 0 \implies (x - 5)(x + 2) = 0$ Roots are $x = 5$ or $x = -2$. Since the argument of a real logarithm must be strictly positive ($x > 3$), $x = -2$ is extraneous. Hence, $x = 5$.
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