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Formula Behavior with Variable Increase

XAT 2014 · Quantitative Ability & Data Interpretation · Easy · Algebra

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Consider the formula, S=α×ωτ+ρ×ωS = \frac{\alpha \times \omega}{\tau + \rho \times \omega} positive integers. If ω\omega is increased and α,τ\alpha, \tau and ρ\rho are kept constant, then S:

  1. A.

    increases

  2. B.

    decreases

  3. C.

    increases and then decreases

  4. D.

    decreases and then increases

  5. E.

    cannot be determined

Answer

A

Explanation

S=αωτ+ρω=ατω+ρS = \frac{\alpha \omega}{\tau + \rho \omega} = \frac{\alpha}{\frac{\tau}{\omega} + \rho}. As ω\omega increases, τω\frac{\tau}{\omega} decreases, so the denominator decreases, and hence SS increases.

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