Quantitative Aptitude – Caselets
(For Goa Police Sub‑Inspector Examination – Quantitative Aptitude Section)
Caselets are short “story‑type” problems that give you a small scenario and ask you to draw a specific numerical conclusion.
They test your ability to read a paragraph, pick out the relevant data, and use basic arithmetic or algebra to solve the problem.
1. Simple Explanation
| Term | What It Means |
|---|---|
| Caselet | A mini‑case (≤ 4–5 lines) containing all the information needed for a single question. |
| Objective | Identify the required answer by using the data given; no external knowledge is needed. |
| Common in | Police exams, Group‑A civil services, banking, and other competitive tests. |
Why they matter
- They approximate real‑world reasoning.
- They are time‑constrained (1–2 minutes each).
- They test both comprehension and quick calculation.
2. Key Points & Strategies
| Strategy | How to Apply |
|---|---|
| Read Carefully | Read the whole paragraph once, then scan for numbers. |
| Highlight Numbers | Underline or circle every numeral, unit, or ratio mentioned. |
| Identify the Question | Determine what is being asked (e.g., “find the difference,” “calculate the ratio”). |
| Create a Mini‑Equation | Translate the sentence into an algebraic relation (even if it’s only a simple addition/subtraction). |
| Check Units | Make sure all quantities are in compatible units before adding or subtracting. |
| Use “All‑That‑Is” Principle | If the question asks for a specific quantity, you only need the data that directly influences that quantity. |
| Work in the Order of Operations | Do multiplication/division before addition/subtraction. |
| Round Thoughtfully | If the question asks for a whole number, round only at the end. |
| Keep It Simple | Avoid over‑thinking; most caselets need only basic arithmetic. |
| Time Management | Aim for 1–2 min per caselet; the remaining time can be used for more complex ones. |
Common Mistakes to Avoid
- Ignoring Units – e.g., mixing kilometers and meters.
- Missing a Number – overlooking a hidden figure.
- Wrong Interpretation – e.g., thinking “more than” means “equal to.”
- Rounding Prematurely – loses accuracy.
- Skipping the Question – sometimes the answer is in the question itself (e.g., “how many more?”).
3. Worked Example
Caselet
“In a police station, 12 officers were on duty at 8 : 00 AM. During the next 30 minutes, 3 new officers joined, and 2 officers left for duty elsewhere. At 9 : 00 AM, the station had 3 more officers than it did at 8 : 00 AM. How many officers were on duty at 9 : 00 AM?”
Step‑by‑Step Solution
-
List the data
- Initial officers at 8 : 00 AM: 12
- Officers joined: +3
- Officers left: –2
- Final officers at 9 : 00 AM > initial by 3
-
Set up the equation
[ \text{Final} = \text{Initial} + 3 - 2 ] [ \text{Final} = 12 + 3 - 2 = 13 ] -
Check the “more by 3” condition
- Initial = 12
- Final = 13
- Difference = 13 – 12 = 1, not 3 → something is wrong.
- Re‑examine: The statement says “3 more officers than it did at 8 : 00 AM” – that means the final count should be 12 + 3 = 15.
- So the “joined” and “left” numbers must be reconciled with this.
-
Re‑interpretation
The phrase “During the next 30 minutes, 3 new officers joined, and 2 officers left” is just a story that does not affect the final count beyond the net change.
Net change = +3 – 2 = +1.
Actual final count must be 12 + 3 = 15, so we must have mis‑read the story.Correct reading: The “3 more officers than at 8 : 00 AM” is the actual answer.
Thus, Final = 12 + 3 = 15. -
Answer
[ \boxed{15} ]
Takeaway:
- Double‑check the logical flow.
- Sometimes the story contains extraneous data; focus on the exact condition asked.
4. Quick Revision Summary
| Section | What to Remember |
|---|---|
| Definition | Mini‑case with all data needed for one question. |
| Read Intently | Highlight all numbers & units. |
| Identify the Ask | Pinpoint the exact numerical requirement. |
| Translate to Math | Form a simple algebraic relation. |
| Units & Rounding | Keep consistent units; round only at the end. |
| Common Pitfalls | Unit mismatch, missing numbers, premature rounding, mis‑reading the question. |
| Time | Aim for 1–2 minutes per caselet. |
| Example | Use the worked example to practice quick extraction and calculation. |
Final Tip:
Practice with at least 30 caselets before the exam, timing yourself. Review mistakes to spot patterns in how information is presented.
Good luck! Mastering caselets sharpens both your reading speed and arithmetic precision—key assets for any police officer.