GMAT Quant: The Concept of “Variation” or “Proportionality”

Quick Summary

On GMAT variation, translate words into equations: direct, inverse, or combined. Write relationships like A ∝ B/C, replace ∝ with a constant k: A = k(B/C). Use given data to find k, substitute new values, and solve. Track exponents, signs, and units carefully throughout.

Overview

Variation questions on the GMAT are a natural extension of ratio and proportion problems, but they demand a deeper understanding of how quantities interact. Unlike simple ratios, variation introduces the idea of constants and proportionality. A quantity may vary directly with another, inversely with a third, or even combine both relationships. The key is to translate these words into precise mathematical expressions and then solve step by step.

For instance, if A varies directly with the square of B and inversely with C, the relationship is written as A ∝ (B² / C). Once the proportionality sign is removed, a constant enters the equation, allowing you to substitute values and solve for unknowns. With careful practice, such questions become straightforward. Strengthening this skill is a valuable part of GMAT prep, and building consistency through GMAT mocks ensures you apply the method confidently under exam conditions

Understanding Variation or Proportionality on GMAT Questions

Variation questions revolve around the concept of proportionality and constants. They often describe how one quantity changes with respect to others, such as directly with one and inversely with another.

Applying the Concept

Question: A varies directly with square of B and inversely with C. When B = 20, C = 5 and A = 100. Find C when A = 60 and B = 8.

Since A varies directly with the square of B and inversely with C, this can be expressed as A ∝ (B² / C).

To convert this into a usable equation, we replace the proportionality with a constant k, giving A = k(B²)/C.

It is given that when B = 20 and C = 5, A = 100.

Substituting these into the equation gives 100 = k(20²)/5.

Solving for k, we find k = 5/4. This establishes the relationship as A = (5/4)(B²)/C.

Now, for A = 60 and B = 8, we substitute these values into the equation:
60 = (5/4)(8²)/C.

Simplifying, we find C = 4/3.

Why This Matters

The strength of this approach lies in its structure. Instead of memorizing shortcuts, you learn to build the relationship from first principles. This prevents errors and gives you clarity, even in more complex variation questions.

Parting Thought

Variation teaches a gentle way to read change. You begin with what holds constant, watch how one part grows while another yields, and choose responses that keep the whole in balance. Life asks the same care. Goals rise, time tightens, tradeoffs appear; you calibrate calmly, step by step. When the path is crowded, a seasoned guide helps you fix the constant and scale the rest. Thoughtful MBA Admission Consulting aligns study, profile, and voice so effort compounds into confident outcomes.