**CAT DILR: Data Comparison – Percentages, Ratios, Growth**

CAT DILR: Data Comparison – Percentages, Ratios, Growth

(Premium Study Guide for 99+ Percentile Aspirants)

What This Is

Data Comparison questions in DILR test your ability to compare quantities (percentages, ratios, growth rates) across tables, graphs, or statements. These appear in ~3-4 questions per CAT (often in sets of 2-3) and are high-scoring if you master the comparison logic instead of full calculations. A typical question:

"Company A’s revenue grew by 20% in 2020 and 25% in 2021. Company B’s revenue grew by 22% in 2020 and 23% in 2021. If both started with the same revenue in 2019, which company had higher revenue in 2021?"

Why it matters: These questions reward speed + accuracy—you can solve them in <1.5 min with the right approach, freeing up time for tougher LR sets.

Key Concepts & Techniques

1. Base Effect Awareness
2. What: Growth percentages are relative to the previous year’s value, not the original base.
3. When to use: When comparing compounded growth (e.g., "20% growth in Year 1 + 25% in Year 2" vs. "22% + 23%").

4. Example: A 50% growth on ₹100 (→ ₹150) is smaller than 20% growth on ₹200 (→ ₹240), even though 50% > 20%.

5. Ratio Comparison via Cross-Multiplication

6. What: To compare a/b vs. c/d, compare a×d vs. b×c (avoids division).
7. When to use: When comparing fractions or ratios (e.g., profit margins, efficiency ratios).

8. Example: Compare 3/5 vs. 4/7 → 3×7 = 21 vs. 5×4 = 20 → 3/5 > 4/7.

9. Percentage Change vs. Absolute Change

10. What: A higher percentage growth doesn’t always mean a larger absolute increase (depends on base value).
11. When to use: When comparing growth rates across different base values (e.g., small vs. large companies).

12. Example: 10% of ₹1000 (₹100) > 50% of ₹100 (₹50).

13. Successive Percentage Changes

14. What: For two successive changes of x% and y%, net change = x + y + (x×y)/100.
15. When to use: When comparing compounded growth over multiple periods.

16. Example: 20% growth + 25% growth = 20 + 25 + (20×25)/100 = 50% net growth.

17. Common Denominator for Ratios

18. What: Convert ratios to a common base (e.g., 100) to compare easily.
19. When to use: When comparing multiple ratios (e.g., market shares, profit splits).

20. Example: Compare 2:3 vs. 3:5 → Convert to 10:15 vs. 9:15 → 2:3 > 3:5.

21. Reverse Percentage Calculations

22. What: If a value increases by x%, to return to the original, it must decrease by x/(100+x) × 100%.
23. When to use: When dealing with discounts, markups, or recovery scenarios.

24. Example: A 25% increase requires a 20% decrease to return to the original (25/125 × 100 = 20%).

25. Indexing for Comparison

26. What: Assign a base value (e.g., 100) to one quantity and scale others proportionally.
27. When to use: When comparing multiple entities with different starting points (e.g., GDP, sales).

28. Example: If Company A’s revenue = ₹200 and Company B’s = ₹300, set A = 100 → B = 150.

29. Approximation for Speed

30. What: Round numbers to nearest 10s/100s to compare quickly (e.g., 47% ≈ 50%, 19% ≈ 20%).
31. When to use: In MCQs where exact calculation isn’t needed (eliminate options).
32. Example: Compare 47/98 vs. 52/103 → Approximate to 47/100 ≈ 0.47 vs. 52/100 ≈ 0.52 → 52/103 > 47/98.

Step-by-Step Strategy

Follow this process for every Data Comparison question:

1. Identify the Quantities to Compare
2. Underline the two (or more) values being compared (e.g., "Company X’s profit in 2020 vs. Company Y’s profit in 2021").

3. Note if they are absolute values, percentages, or ratios.

4. Check for Common Bases

5. If the quantities have different starting points, convert them to a common base (e.g., index to 100, or express as ratios).

6. Example: If comparing 20% of 500 vs. 25% of 400, calculate both (100 vs. 100).

7. Apply the Right Comparison Tool

8. Percentages: Use successive change formula or base effect.
9. Ratios: Use cross-multiplication or common denominator.

10. Growth Rates: Compare net growth (not individual percentages).

11. Eliminate Impossible Options

12. In MCQs, rule out options that violate logic (e.g., "Company A’s growth is higher but its revenue is lower").

13. Use approximation to quickly discard wrong answers.

14. Calculate Only if Necessary

15. Avoid full calculations unless two options are very close.

16. For TITA questions, derive the exact relationship (e.g., "A > B" or "A = B").

17. Verify with a Quick Check

18. Plug in simple numbers to test your logic (e.g., assume revenue = ₹100 for both companies).
19. If the answer seems counterintuitive, re-examine the base effect.

Fully Worked CAT-Style Example

Question:
In 2019, the revenues of Company P and Company Q were equal. In 2020, P’s revenue grew by 10% and Q’s by 20%. In 2021, P’s revenue grew by 20% and Q’s by 10%. Which company had higher revenue in 2021?

Solution (Using the Strategy):

1. Identify Quantities to Compare:
2. Compare P’s 2021 revenue vs. Q’s 2021 revenue.

3. Both started equal in 2019.

4. Check for Common Bases:

5. Let 2019 revenue = ₹100 (common base).

6. Apply Comparison Tool (Successive Growth):

7. Company P:
   • 2020: 10% growth → ₹100 × 1.10 = ₹110
   • 2021: 20% growth → ₹110 × 1.20 = ₹132

8. Company Q:

   
   
   • 2020: 20% growth → ₹100 × 1.20 = ₹120
   • 2021: 10% growth → ₹120 × 1.10 = ₹132

9. Eliminate Options:

10. If this were an MCQ, options like "P > Q" or "Q > P" would be eliminated immediately.

11. Calculate (if needed):

12. Both reach ₹132 → P = Q.

13. Quick Check:

14. Net growth for P: 10 + 20 + (10×20)/100 = 32%
15. Net growth for Q: 20 + 10 + (20×10)/100 = 32%
16. Confirms P = Q.

Answer: Both companies had equal revenue in 2021.

Common Mistakes

1. Mistake: Assuming higher individual growth rates always lead to higher final value.
2. Why it happens: Ignoring compounding and base effect.

3. Correct approach: Calculate net growth or use successive percentage formula.

4. Mistake: Comparing percentages without considering absolute values.

5. Why it happens: Overlooking that 50% of 100 < 10% of 1000.

6. Correct approach: Always multiply percentage by base value before comparing.

7. Mistake: Misapplying reverse percentages (e.g., thinking a 20% increase requires a 20% decrease to revert).

8. Why it happens: Confusing percentage of original vs. new value.

9. Correct approach: Use x/(100+x) × 100% for reverse calculations.

10. Mistake: Not indexing to a common base when comparing ratios.

11. Why it happens: Comparing 2:3 vs. 3:4 directly without converting to a common denominator.

12. Correct approach: Convert to 8:12 vs. 9:12 → 2:3 < 3:4.

13. Mistake: Over-calculating in MCQs.

14. Why it happens: Not using approximation or option elimination.
15. Correct approach: Round numbers and eliminate impossible options first.

CAT Traps & Time Management

Traps to Watch For:

1. Hidden Base Changes:
2. Trap: A question might say "Company A’s profit grew by 30% in 2020 and 20% in 2021," but the base for 2021 is 2020’s profit, not 2019’s.

3. How to avoid: Always track the base year for each percentage.

4. Ratio vs. Absolute Value Confusion:

5. Trap: A question might ask, "Which company has a higher profit margin?" but provide absolute profits instead of ratios.

6. How to avoid: Read the question carefully—profit margin = profit/revenue, not just profit.

7. Successive Discounts/Markups:

8. Trap: A 10% discount followed by a 20% discount is not 30% (it’s 10 + 20 - (10×20)/100 = 28%).

9. How to avoid: Use the successive percentage formula.

10. Non-Linear Growth:

11. Trap: Assuming growth is linear (e.g., "If revenue grew by 10% in 2 years, it grew by 5% per year").
12. How to avoid: Use compound growth formula (Final = Initial × (1 + r)^n).

Time Management:

• Easy/Medium Questions: 1–1.5 min (use approximation, eliminate options).
• Hard Questions: 2–2.5 min (full calculation only if necessary).
• TITA Questions: 2 min max (derive exact relationship, no guessing).

Quick Practice

Question 1:
In 2020, the ratio of boys to girls in a school was 3:4. In 2021, the number of boys increased by 20% and girls by 10%. What is the new ratio of boys to girls in 2021? Answer: 9:11 Solution Path:
- Assume 2020: Boys = 300, Girls = 400.
- 2021: Boys = 300 × 1.20 = 360, Girls = 400 × 1.10 = 440.
- New ratio = 360:440 = 9:11.

Question 2:
Company X’s revenue grew by 15% in 2020 and 25% in 2021. Company Y’s revenue grew by 20% in 2020 and 20% in 2021. If both started with the same revenue in 2019, which company had higher revenue in 2021? Answer: Company X
Solution Path:
- Net growth for X: 15 + 25 + (15×25)/100 = 43.75% - Net growth for Y: 20 + 20 + (20×20)/100 = 44% - Wait! This seems contradictory—recheck: - X: 1.15 × 1.25 = 1.4375 (43.75%) - Y: 1.20 × 1.20 = 1.44 (44%) - Y > X (Trap: Higher individual growth doesn’t always win—base effect matters).

Last-Minute Cram Sheet

1. Successive % changes: x + y + (x×y)/100 (for increases; subtract for decreases).
2. Reverse %: If value increases by x%, to revert, decrease by x/(100+x) × 100%.
3. Ratio comparison: Cross-multiply (a/b > c/d if a×d > b×c).
4. Common base: Index to 100 for easy comparison.
5. Higher % growth ≠ higher absolute value (check base!).
6. Approximate: Round to nearest 10s/100s for speed.
7. Trap: Successive discounts ≠ sum of discounts.
8. Trap: Growth rates are relative to previous year, not original base.
9. TITA questions: Derive exact relationship (no guessing).
10. Time: 1–1.5 min for easy, 2–2.5 min for hard.

Final Tip: In DILR, comparison questions are about logic, not calculation. Master the base effect, ratios, and successive changes—and you’ll solve them faster than 90% of test-takers.