📚 APO Exam – Quantitative Aptitude
Topic: Caselets
Caselets are short, real‑life scenario questions that combine a few quantitative concepts.
They test your ability to:
- Read quickly and identify the data.
- Choose the right formula or method.
- Compute accurately (often under 2–3 minutes).
Below is a concise guide to master caselets for the APO exam.
1. Simple Explanation
| What is it? | Why it matters | When you’ll see it |
|---|---|---|
| A caselet is a brief, descriptive passage followed by a quantitative question. | It mirrors real‑life problems; the examiners want you to apply logic and math, not memorize. | 25–35% of the Quant section in many aptitude tests. |
2. Key Points & Strategies
| # | Key Point | Practical Tip | Example |
|---|---|---|---|
| 1. Skim First | Read the passage once, then underline or highlight numbers. | Don’t get lost in the story. | In “A shop sold 120 phones, 30% were premium.” |
| 2. Identify the Question Type | Average, ratio, percentage change, time‑distance, profit‑loss, mixture, etc. | Use the keyword list below. | “If the total profit is 10% of cost.” |
| 3. Convert All Units | Align units (days ↔ hours, km ↔ miles). | Convert once, stay consistent. | “Speed = 60 km/h → 100 km → 1.67 h.” |
| 4. Use “Assume” or “Let” | Introduce variables for unknowns. | Keeps arithmetic clean. | Let x = total cost. |
| 5. Work Backwards | Start from the information you know most directly. | Reduces unnecessary steps. | Compute average of group A first. |
| 6. Check for “All Numbers Are Int” | If the answer must be an integer, round only after all calculations. | Avoid early rounding errors. | 75 ÷ 4 = 18.75 → keep decimals till final. |
| 7. Mental Math Hacks | - Break fractions into parts (e.g., 3/4 = 0.75). - Use “10‑rule” for percentages (10% of 200 = 20). |
Saves time. | “10% of 3,600 = 360.” |
| 8. Verify with Quick Estimation | Roughly estimate to see if the answer is plausible. | Catch computational slips. | If average 90% for 12 students vs overall 75% → below‑80% average should be < 75. |
| 9. Use Tables | Tabulate data for clarity (especially in mixture or time‑distance). | Reduces confusion. | Table of speeds, distances, times. |
| 10. Practice “What If” Scenarios | Change one variable and see impact. | Helps in data sufficiency or sensitivity questions. | If 10% more students scored above 80%, how would overall average change? |
Common Question Types in Caselets
| Category | Typical Problem | Formula(s) |
|---|---|---|
| Average | “A class of 30 students scored an average of 70. 5 students scored 90. What is the average of the remaining 25?” | Avg = Total / No. of students |
| Ratio & Proportion | “The ratio of boys to girls is 3:2. If there are 30 boys, how many girls?” | Boys / Girls = 3/2 |
| Percentage Change | “A product’s price increased by 20% and then decreased by 10%. What is the net change?” | New = Old × (1 + r1) × (1 – r2) |
| Time & Distance | “A train travels 120 km in 2 hrs. How long to travel 180 km at the same speed?” | Time = Distance / Speed |
| Profit & Loss | “A shop sells an item at a 15% profit on cost price of ₹200.” | Selling Price = Cost × (1 + Profit%) |
| Mixture | “Blend 3 liters of 30% solution with 5 liters of 50% solution. Find concentration.” | Result % = (V1×P1 + V2×P2)/(V1+V2) |
| Algebraic Equations | “If x > y > z and x + y + z = 12, find x if x = 2y.” | Solve linear equations |
| Data Sufficiency | “Is the information enough to determine the average?” | Evaluate two conditions (A) & (B) |
3. Worked Example (Caselet)
Caselet
In a school, 18 students scored above 80%, and 12 scored below 80%.
The average score of the above‑80% group is 90%.
The overall average score of the class is 75%.
Question: What is the average score of the below‑80% group?
Step‑by‑Step Solution
| Step | Explanation | Calculation |
|---|---|---|
| 1. Define Variables | Let A = average of below‑80% group. |
— |
| 2. Compute Total Scores | Total = (Number × Average). | `Total = 18×90 + 12× |