GMAT Focus Edition — Data Insights: Table Analysis · Graphics Interpretation · Multi-Source Reasoning · Two-Part Analysis
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Data Insights Lesson 19 of 20

Lesson 19:
Ratio Analysis & Visual Proportions

Read and interpret ratios from charts and tables. Convert ratios to fractions, decimals, and percentages. Solve ratio word problems from visual data.

⏱ 50 mins
🎯 DI 75 to 88
📚 Prereq: Lesson 17 (Percentages)
Note: Lesson 19 of 20 — Ratio Analysis & Visual Proportions.
1

Core Concepts: Ratio Analysis & Visual Proportions

Read and interpret ratios from charts and tables. Convert ratios to fractions, decimals, and percentages. Solve ratio word problems from visual data.

Key Framework
Ratio a:b → fraction a/(a+b)
Convert ratio to fraction of total by dividing each part by the sum of parts.
Cross-multiply for equivalent ratios
If 3:5 = x:20, then x = 3×20/5 = 12.
Ratio charts: gaps and proportions
In bar charts showing ratios, the relative bar heights give the ratio directly.
Ratio change: use algebra, not visual estimation
If ratio changes from 2:3 to 3:4, compute numerically — visual proportions mislead.
2

Application Strategy

Step-by-Step Approach
①
Identify the question type and the specific metric being asked about.
②
Locate the relevant data in the chart, table, or tab.
③
Apply the key formula or logic rule from the framework above.
④
Verify that your answer satisfies the question as stated.
3

Visual Reference Diagram

Visual Framework for Lesson 19
📊
Ratio a:b → fraction a/(a+b)
📈
Cross-multiply for equivalent ratios
🔍
Ratio charts: gaps and proportions
📋
Ratio change: use algebra, not visual estimation
4

Quick Reference Rules

▸
Ratio a:b → fraction a/(a+b): Convert ratio to fraction of total by dividing each part by the sum of parts.
▸
Cross-multiply for equivalent ratios: If 3:5 = x:20, then x = 3×20/5 = 12.
▸
Ratio charts: gaps and proportions: In bar charts showing ratios, the relative bar heights give the ratio directly.
▸
Ratio change: use algebra, not visual estimation: If ratio changes from 2:3 to 3:4, compute numerically — visual proportions mislead.
5

10 Traps for Lesson 19

⚠ Confusing the key formula for this topic

Review the core rule: Ratio a:b → fraction a/(a+b)

⚠ Reading the wrong data series

Always verify axis labels and legends before extracting values.

⚠ Ignoring units or scale

Check units on every axis before computing ratios or changes.

⚠ Treating estimates as exact

GI data requires interpolation — use approximate values and pick the closest answer.

⚠ Forgetting the denominator

Cross-multiply for equivalent ratios — always identify what you're dividing by.

⚠ Applying simple average when weighted is needed

If group sizes differ, compute weighted average, not simple mean.

⚠ "All" statements need every row verified

One counterexample makes a universal statement False.

⚠ Scope: data sample ≠ full population

Conclusions are limited to the data range provided, not broader populations.

⚠ Confusing absolute and relative measures

Absolute change ($) and relative change (%) answer different questions.

⚠ Not using the complement when helpful

P(at least one) = 1 − P(none). In set logic, use complement for "not" conditions.

✦

10 Practice Questions

Q1 of 10
GI~600

The ratio of blue to red balls in a bag is 3:5. If there are 24 blue balls, how many red balls are there?

Explanation: 40. 3/5 = 24/x → x = 24×5/3 = 40.
Q2 of 10
GI~600

A pie chart shows A:B:C in ratio 2:3:5. If total = 400, how many are in B?

Explanation: 120. B's fraction = 3/(2+3+5) = 3/10. B = 3/10 × 400 = 120.
Q3 of 10
GI~600

Two quantities are in the ratio 4:7. If the larger is 63, the smaller is:

Explanation: 36. 4/7 = x/63 → x = 4×63/7 = 36.
Q4 of 10
GI~550

A bar chart shows revenue for Dept A and B in ratio 5:3. Dept A = $150M. Dept B = ?

Explanation: $90M. 5/3 = 150/B → B = 150×3/5 = $90M.
Q5 of 10
GI~600

If the ratio of men to women in a company is 3:2, and there are 120 men, total employees = ?

Explanation: 200. Men = 3 parts = 120, so 1 part = 40. Total = 5 parts = 200.
Q6 of 10
GI~750

A line graph shows two companies' revenue in ratio 3:1 in Year 1 and 5:2 in Year 5. Which company gained more share (as a fraction of combined)?

Explanation: Company B gained relative share. Year 1 B share = 1/4 = 25%. Year 5 B share = 2/7 ≈ 28.6%. B's fractional share increased. A's share = 3/4 = 75% → 5/7 ≈ 71.4%, which decreased.
Q7 of 10
GI~650

A map uses a scale ratio of 1:50,000. If two cities are 3 cm apart on the map, actual distance = ?

Explanation: 1.5 km. 3 cm × 50,000 = 150,000 cm = 1,500 m = 1.5 km.
Q8 of 10
GI~550

In a table, Company X's profit-to-revenue ratio is 0.15 and revenue is $200M. Profit = ?

Explanation: $30M. Profit = ratio × revenue = 0.15 × $200M = $30M.
Q9 of 10
GI~650

A data table shows cost ratios across 5 projects. Project C has the highest cost-to-output ratio. This means:

Explanation: Project C is the least efficient. A high cost-to-output ratio means more cost is spent per unit of output — indicating inefficiency. The most efficient project has the LOWEST cost-to-output ratio.
Q10 of 10
GI~600

A ratio of 5:4 is equivalent to which percentage split?

Explanation: 55.6% / 44.4%. Total parts = 9. First part = 5/9 ≈ 55.6%. Second part = 4/9 ≈ 44.4%.
Lesson Summary
Ratio a:b → fraction a/(a+b)

Convert ratio to fraction of total by dividing each part by the sum of parts.

Cross-multiply for equivalent ratios

If 3:5 = x:20, then x = 3×20/5 = 12.

Ratio charts: gaps and proportions

In bar charts showing ratios, the relative bar heights give the ratio directly.

Ratio change: use algebra, not visual estimation

If ratio changes from 2:3 to 3:4, compute numerically — visual proportions mislead.

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