Line Graph DI — Trends, Slopes & Derived Values
Decode single and double line graphs. Learn to read trends, derive third variables, and handle negative percentage relationships.
Line Graph DI — Trends, Slopes & Derived Values
Line graphs show data points connected by lines, making them ideal for displaying trends over time or across categories. In banking exams, line graph DI sets frequently combine two line graphs to test your ability to derive a third variable.
| Line Graph Type | What It Shows |
|---|---|
| Single Line | One dataset across categories (e.g., production over years) |
| Double Line | Two datasets on the same axes (e.g., import vs export) |
| Derived Line | Second line graph gives a percentage relationship to compute a hidden variable |
Reading Trends and Slopes
Before diving into calculations, spend 5 seconds scanning the graph for:
- Upward slope = increasing trend
- Downward slope = decreasing trend
- Steep slope = rapid change (large difference between consecutive points)
- Flat line = no change or very small change
- Crossing point = two datasets become equal at that point
Exam Tip: Some questions ask "In which year was the increase maximum?" or "Between which two years was the decline sharpest?" These require no calculation — just look for the steepest slope segment.
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Line Graph DI — Trends, Slopes & Derived Values
Line graphs show data points connected by lines, making them ideal for displaying trends over time or across categories. In banking exams, line graph DI sets frequently combine two line graphs to test your ability to derive a third variable.
| Line Graph Type | What It Shows |
|---|---|
| Single Line | One dataset across categories (e.g., production over years) |
| Double Line | Two datasets on the same axes (e.g., import vs export) |
| Derived Line | Second line graph gives a percentage relationship to compute a hidden variable |
Reading Trends and Slopes
Before diving into calculations, spend 5 seconds scanning the graph for:
- Upward slope = increasing trend
- Downward slope = decreasing trend
- Steep slope = rapid change (large difference between consecutive points)
- Flat line = no change or very small change
- Crossing point = two datasets become equal at that point
Exam Tip: Some questions ask "In which year was the increase maximum?" or "Between which two years was the decline sharpest?" These require no calculation — just look for the steepest slope segment.
Double Line Graphs: Deriving a Third Variable
The most common exam pattern:
- Line 1 gives values of Item X (e.g., Books sold)
- Line 2 gives values of Item Y (e.g., Copies sold)
- A separate line graph gives "% of Item Z more/less than Item Y"
You must use all three to find Item Z.
Worked Example: Books, Copies, and Pencils
Line Graph 1 — Items sold by sellers P through T:
| Seller | Books | Copies |
|---|---|---|
| P | 200 | 165 |
| Q | 325 | 300 |
| R | 500 | 270 |
| S | 400 | 140 |
| T | 400 | 204 |
Line Graph 2 — Percentage of pencils sold more/less than copies:
| Seller | P | Q | R | S | T |
|---|---|---|---|---|---|
| % | -33.33% | -20% | +16.66% | +25% | +66.66% |
Critical Concept: Negative Percentages
A negative percentage means pencils are LESS than copies. A positive percentage means pencils are MORE than copies.
This is the number one trap in line graph DI. Many students misread "-33.33%" as "33.33% more" and get the wrong answer.
- Negative: Pencils = Copies - (percentage of Copies) = Copies x (1 - %/100)
- Positive: Pencils = Copies + (percentage of Copies) = Copies x (1 + %/100)
Step-by-step: Finding Pencils for Each Seller
Seller P: Pencils are 33.33% LESS than Copies
- 33.33% = 1/3
- Pencils = 165 x (1 - 1/3) = 165 x 2/3 = 110
Seller Q: Pencils are 20% LESS than Copies
- 20% = 1/5
- Pencils = 300 x (1 - 1/5) = 300 x 4/5 = 240
Seller R: Pencils are 16.66% MORE than Copies
- 16.66% = 1/6
- Pencils = 270 x (1 + 1/6) = 270 x 7/6 = 315
Seller S: Pencils are 25% MORE than Copies
- 25% = 1/4
- Pencils = 140 x (1 + 1/4) = 140 x 5/4 = 175
Seller T: Pencils are 66.66% MORE than Copies
- 66.66% = 2/3
- Pencils = 204 x (1 + 2/3) = 204 x 5/3 = 340
Complete Data Table
| Seller | Books | Copies | Pencils |
|---|---|---|---|
| P | 200 | 165 | 110 |
| Q | 325 | 300 | 240 |
| R | 500 | 270 | 315 |
| S | 400 | 140 | 175 |
| T | 400 | 204 | 340 |
Essential Fraction Conversions for Line Graph DI
These recurring percentages appear in almost every DI set. Memorize the fraction form — it eliminates all decimal work.
| Percentage | Fraction | "X% more" = multiply by | "X% less" = multiply by |
|---|---|---|---|
| 11.11% | 1/9 | 10/9 | 8/9 |
| 12.5% | 1/8 | 9/8 | 7/8 |
| 14.28% | 1/7 | 8/7 | 6/7 |
| 16.66% | 1/6 | 7/6 | 5/6 |
| 20% | 1/5 | 6/5 | 4/5 |
| 25% | 1/4 | 5/4 | 3/4 |
| 33.33% | 1/3 | 4/3 | 2/3 |
| 37.5% | 3/8 | 11/8 | 5/8 |
| 40% | 2/5 | 7/5 | 3/5 |
| 50% | 1/2 | 3/2 | 1/2 |
| 66.66% | 2/3 | 5/3 | 1/3 |
Speed Trick: When you see 33.33% in the graph, your hand should automatically write "x 1/3" (for less) or "x 4/3" (for more). Never convert 33.33% to 0.3333 and multiply — that wastes 15-20 seconds per calculation.
Worked Question: External Variable with Ratios
Question: Pencils sold by P = 20% of erasers sold by P. The ratio of erasers sold by P to erasers sold by Q is 5:4. Find the difference between erasers sold by Q and copies sold by Q.
Step-by-step:
Step 1: Find erasers sold by P.
- Pencils by P = 110 (from our table)
- 110 = 20% of erasers by P
- Erasers by P = 110 / 0.20 = 110 x 5 = 550
Shortcut: 20% = 1/5, so if pencils = 1/5 of erasers, then erasers = pencils x 5 = 550
Step 2: Find erasers sold by Q.
- Ratio of erasers P : Q = 5 : 4
- Erasers Q = 550 x 4/5 = 440
Step 3: Find the difference.
- Copies by Q = 300 (from the table)
- Difference = 440 - 300 = 140
Answer: 140
Common Traps in Line Graph DI
Trap 1: Mixing Up "More" and "Less"
When the percentage is negative, students often still add. Always check the sign.
| Graph shows | Meaning | Formula |
|---|---|---|
| +25% | Pencils are 25% MORE than Copies | Pencils = Copies x 5/4 |
| -25% | Pencils are 25% LESS than Copies | Pencils = Copies x 3/4 |
Trap 2: "% more than" vs "% of"
These are different:
- "A is 20% more than B" means A = B x 6/5
- "A is 20% of B" means A = B x 1/5
Confusing these gives answers that are off by a factor of 6.
Trap 3: Wrong Base for Percentage
- "A is what % more than B?" → Base is B: ((A-B)/B) x 100
- "B is what % less than A?" → Base is A: ((A-B)/A) x 100
These give different answers even though the absolute difference (A-B) is the same.
Example: A = 150, B = 120. "A is what % more than B?" = (30/120) x 100 = 25% "B is what % less than A?" = (30/150) x 100 = 20%
Trend-Based Questions (No Calculation Needed)
Some questions test observation, not arithmetic:
- "For how many sellers is the number of pencils greater than books?" — Just compare the two columns.
- "Which seller shows the maximum difference between books and copies?" — Scan and estimate.
- "Between which two consecutive sellers does the copies line show the steepest decline?" — Look at the slope.
Exam Tip: Answer these first. They take 10-15 seconds each and are free marks.
Summary
- Scan the line graph for trends before reading questions — note peaks, dips, and crossings.
- Negative percentages = LESS, positive percentages = MORE. This is the most common error.
- Convert percentages to fractions instantly (33.33% = 1/3, 16.66% = 1/6, 66.66% = 2/3).
- For "% more": multiply by (denominator + numerator) / denominator. For "% less": multiply by (denominator - numerator) / denominator.
- Build only the cells you need from the data table — not the entire table.
- Watch for the base trap in "% more than" vs "% less than" questions.
Summary Cheat Sheet
| Concept / Topic | Key Details / Explanation |
|---|---|
| Line graph types | Single (one dataset), Double (two datasets), Derived (third line gives % relationship to compute hidden variable) |
| Trend reading | Upward slope = increasing, Downward = decreasing, Steep = rapid change, Flat = no change, Crossing point = two datasets equal |
| Trend questions (no calculation) | "In which year was increase maximum?" → find steepest slope. Answer in 10–15 seconds |
| Negative percentage = LESS | If graph shows −33.33%, pencils are LESS than copies. Most common trap |
| Positive percentage = MORE | If graph shows +25%, pencils are MORE than copies |
| Formula: % LESS | Pencils = Copies × (1 − %/100). E.g., −33.33% → Copies × 2/3 |
| Formula: % MORE | Pencils = Copies × (1 + %/100). E.g., +16.66% → Copies × 7/6 |
| 33.33% fraction | 1/3. Less → × 2/3. More → × 4/3 |
| 16.66% fraction | 1/6. Less → × 5/6. More → × 7/6 |
| 66.66% fraction | 2/3. Less → × 1/3. More → × 5/3 |
| 25% fraction | 1/4. Less → × 3/4. More → × 5/4 |
| "% more than" vs "% of" | "A is 20% more than B" = B × 6/5. "A is 20% of B" = B × 1/5. Confusing these is off by factor of 6 |
| Base trap | "A what % more than B?" base = B. "B what % less than A?" base = A. Same A−B, different answers |
| External variable with ratio | If pencils = k% of erasers → erasers = pencils / (k/100) = pencils × (100/k). Then apply ratio to find related values |
| Don't pre-build the full table | Compute only cells the question needs — saves 1–2 minutes per set |
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