Ratios are a fundamental concept in GMAT Quant, testing your ability to understand relationships and manipulate values efficiently. This guided path will take you from the core principles to the advanced strategies and shortcuts needed for a top score.
Start with the core definition and walk through a step-by-step example of how to simplify ratios to their lowest terms.
A ratio compares values. Always express it in simplest form (like a fraction).
Car Zippy: $37,500
Car Giffy: $32,500
Ratio Z : G?
Divide by 100:
$$ 375 : 325 $$Both end in 5. Divide by 25:
$$ 375 \div 25 = 15 $$
$$ 325 \div 25 = 13 $$
Final Ratio: 15 : 13
Learn the fundamental method for solving word problems by representing unknown values with a common multiplier 'x'.
Multiply a ratio by a constant. The value remains the same.
Master the methods for distributing a total amount into a given ratio and for working backwards to find the total from a single part.
Master the crucial technique for combining two separate ratios (e.g., a:b and b:c) into a single, continuous ratio (a:b:c).
Walk through a real-world application of ratios in partnership problems, where both investment and time must be considered.
When investment periods differ, profit is shared in the Compound Ratio of (Capital × Time).
A invests \$10k for 4 months.
B invests \$20k for 6 months.
C invests \$30k for 12 months.
Profit: \$7800.
Ratio: $$ 2:6:18 \rightarrow 1:3:9 $$
Total Parts: $$ 1+3+9 = 13 $$
1 Part = $$ 7800/13 = \$600 $$
A: \$600 | B: \$1800 | C: \$5400
Learn how to convert statements of multiples (e.g., 3A = 4B) into the correct A:B ratio, a common trap in advanced problems.
If 3A = 4B, what is A:B?
Rule: Inverse the coefficients.
$$ A:B = 4:3 $$If 2A = 3B = 4C, find A:B:C.
Step 1: Invert coefficients: $$ \frac{1}{2} : \frac{1}{3} : \frac{1}{4} $$
LCM of denominators (2, 3, 4) is 12.
Multiply each fraction by 12.
A: $$ \frac{1}{2} \times 12 = 6 $$
B: $$ \frac{1}{3} \times 12 = 4 $$
C: $$ \frac{1}{4} \times 12 = 3 $$
A:B:C = 6 : 4 : 3
Apply your knowledge to the most unique GMAT question type. Learn to distinguish between questions asking for a ratio vs. a value.
What is the value of x?
$$ x/y = 3/4 $$. Ratio given, but no value. x could be 3, 6, 30... INSUFFICIENT.
$$ y = 12 $$. No info about x. INSUFFICIENT.
Substitute y=12 into ratio:
$$ x/12 = 3/4 \implies x = 9 $$.
Unique value found. SUFFICIENT.
Answer: (C)
Test your ability to solve for the "fourth proportional" and find the "mean proportional," key skills for certain problem types.
Two ratios are equal.
$$ a:b = c:d \implies \frac{a}{b} = \frac{c}{d} $$a, b, c are linked.
$$ a:b = b:c \implies b^2 = ac $$Explore the advanced properties of equal ratios that can be used as powerful shortcuts in the toughest GMAT questions.
If $$ \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = k $$, then:
Sum of Numerators / Sum of Denominators = Original Ratio
Put your understanding of GMAT Ratio & Proportion: A Guide to Advanced Problem Solving to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
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