Numerical Reasoning
"Tol! Numerical Reasoning. Headcount at statistics ng PDL. Accurate math = proper jail management. Hindi pwede mali-mali ang count!"
1. Basic Arithmetic Operations ➕➖
Tol, foundation ng math ay ang basic operations. Dapat accurate lagi - hindi pwede mali ang headcount!
Order of Operations (PEMDAS):
Parentheses - ( ) first
Exponents - powers, roots
Multiplication ×
Division ÷
Addition +
Subtraction −
Example: 10 + 5 × 2 = ?
Step 1: 5 × 2 = 10 (multiplication first)
Step 2: 10 + 10 = 20
Fractions Quick Reference:
| Operation | Rule | Example |
|---|---|---|
| Addition | Common denominator | 1/4 + 1/4 = 2/4 = 1/2 |
| Subtraction | Common denominator | 3/5 - 1/5 = 2/5 |
| Multiplication | Multiply across | 2/3 × 1/2 = 2/6 = 1/3 |
| Division | Flip & multiply | 1/2 ÷ 1/4 = 1/2 × 4/1 = 2 |
2. Ratio & Proportion 📊
Critical sa jail management - PDL to guard ratio, food allocation, etc.
Ratio Basics:
PDL to Guard Ratio Example:
If there are 100 PDLs and 10 guards, the ratio is:
100:10 = 10:1 (10 PDLs per guard)
Simplifying Ratios:
Find the GCD (Greatest Common Divisor)
24:36 → GCD is 12 → 24÷12:36÷12 = 2:3
Direct vs Inverse Proportion:
Direct Proportion:
When one increases, the other increases
More PDLs = More food needed
Inverse Proportion:
When one increases, the other decreases
More guards = Less time for patrol
Cross Multiplication Example:
If 5 guards can search 100 cells in 4 hours, how many hours for 10 guards?
5 × 4 = 10 × x → 20 = 10x → x = 2 hours
3. Percentage Calculations 📈
Important for statistics - congestion rate, rehabilitation completion rate, etc.
Percentage Formulas:
Finding Percentage:
Percentage = (Part / Whole) × 100
50 released out of 200 PDLs: (50/200) × 100 = 25%
Finding the Part:
Part = (Percentage × Whole) / 100
30% of 500 PDLs need medical attention: (30 × 500) / 100 = 150 PDLs
Jail Congestion Rate:
Congestion Rate = (Actual Population / Ideal Capacity) × 100
If 500 PDLs in 100-capacity jail: (500/100) × 100 = 500% congestion
Percentage Increase/Decrease:
Change % = ((New - Old) / Old) × 100
Example:
PDL population changed from 400 to 520. What's the increase?
((520 - 400) / 400) × 100 = (120/400) × 100 = 30% increase
4. Number Series Patterns 🔢
Common sa aptitude tests - identify ang pattern!
Common Pattern Types:
Arithmetic (Add/Subtract constant):
3, 7, 11, 15, 19 (add 4)
25, 22, 19, 16, 13 (subtract 3)
Geometric (Multiply/Divide constant):
2, 4, 8, 16, 32 (multiply by 2)
81, 27, 9, 3, 1 (divide by 3)
Square/Cube Numbers:
1, 4, 9, 16, 25 (perfect squares: 1², 2², 3², 4², 5²)
1, 8, 27, 64, 125 (cubes: 1³, 2³, 3³, 4³, 5³)
Fibonacci-type:
1, 1, 2, 3, 5, 8 (each = sum of previous two)
Alternating Pattern:
2, 6, 4, 8, 6, 10 (+4, -2, +4, -2, +4)
5. Jail Management Math Applications 🏢
Daily Headcount Calculation:
Formula:
End Count = Start Count + Admissions - Releases - Transfers Out + Transfers In
Example: Start = 450, Admitted = 15, Released = 8, Transferred Out = 5, Transferred In = 3
End Count = 450 + 15 - 8 - 5 + 3 = 455
Food Ration Calculation:
Per PDL Allocation:
If budget is P50 per PDL per day for 500 PDLs:
Daily Budget = 500 × P50 = P25,000
Monthly Budget = P25,000 × 30 = P750,000
Guard Shift Scheduling:
24-hour coverage with 8-hour shifts:
If you need 10 guards per shift for 3 shifts:
Minimum guards = 10 × 3 = 30 guards
With day-off rotation: 30 × 1.2 = 36 guards needed
6. Practice Questions 📋
1. If a jail has 300 PDLs and capacity for 100, what is the congestion rate?
A) 200% B) 300% C) 33% D) 150%
View Answer
Answer: B) 300%
Congestion = (300/100) × 100 = 300%
2. What is the next number: 5, 10, 20, 40, ___?
A) 50 B) 60 C) 80 D) 100
View Answer
Answer: C) 80
Pattern: Each number is multiplied by 2. 40 × 2 = 80
3. If 6 guards can search 120 cells in 4 hours, how many guards are needed to search 120 cells in 2 hours?
A) 3 B) 8 C) 10 D) 12
View Answer
Answer: D) 12
Inverse proportion: 6 × 4 = x × 2 → 24 = 2x → x = 12 guards
4. 25% of PDLs completed livelihood training. If there are 400 PDLs, how many completed training?
A) 75 B) 100 C) 125 D) 150
View Answer
Answer: B) 100
25% of 400 = (25/100) × 400 = 100 PDLs
5. The ratio of male to female PDLs is 4:1. If there are 500 total PDLs, how many are female?
A) 80 B) 100 C) 125 D) 400
View Answer
Answer: B) 100
4:1 ratio means 5 parts total. Female = 1/5 × 500 = 100
7. Exam Strategy Tips 🎯
- 🔢 Memorize formulas - Percentage, ratio, number series patterns
- ⏱️ Practice mental math - Faster calculation = more time for hard problems
- 📝 Write it down - Don't try to solve complex problems mentally
- ✅ Check your work - Verify answers by substituting back
- 🧮 Estimate first - Eliminate obviously wrong answers
- 🔄 Know inverse proportion - More workers = less time
Test Your Knowledge! 🧠
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