Quantitative Reasoning
"Tol! Math sa Police Exam? Yes, kailangan mo mag-compute ng distance, time, crime rate, at marami pang stats! Numbers ang katotohanan sa law enforcement!"
1. Basic Arithmetic Operations ➕➖✖️➗
Foundation ng lahat ng math problems. Dapat mabilis at accurate!
Order of Operations (PEMDAS/BODMAS):
Parentheses / Brackets - First
Exponents / Orders - Second
Multiplication & Division - Left to right
Addition & Subtraction - Left to right
Example:
5 + 3 × 2 = ?
❌ Wrong: 16 (adding first)
✅ Correct: 11 (multiply first)
2. Fractions, Decimals & Percentages 📊
Conversion between these is crucial for police statistics!
Fraction
1/4
Decimal
0.25
Percentage
25%
🔄 Conversion Formulas:
- • Fraction → Decimal: Divide numerator by denominator
- • Decimal → Percentage: Multiply by 100
- • Percentage → Decimal: Divide by 100
- • Percentage → Fraction: Put over 100, simplify
📈 Percentage Problems:
Finding Percentage:
What is 15% of 200? → 0.15 × 200 = 30
Finding the Whole:
30 is 15% of what? → 30 ÷ 0.15 = 200
Finding the Rate:
30 is what percent of 200? → (30 ÷ 200) × 100 = 15%
3. Distance, Speed, Time: The Police Triangle 🚓
Tol, pursuit situations require quick calculations!
The DST Triangle
D
Distance
D = S × T
S
Speed
S = D ÷ T
T
Time
T = D ÷ S
🚔 Police Scenario Examples:
Example 1:
A patrol car travels 120 km in 2 hours. What is the average speed?
S = D ÷ T = 120 ÷ 2 = 60 km/h
Example 2:
A suspect is running at 15 km/h. How far will he go in 20 minutes?
D = S × T = 15 × (20/60) = 15 × 0.33 = 5 km
Example 3:
Reinforcement is 30 km away, traveling at 60 km/h. ETA?
T = D ÷ S = 30 ÷ 60 = 0.5 hours = 30 minutes
4. Ratio and Proportion 📐
Para sa resource allocation, manpower distribution, at statistics!
Ratio:
Comparison of two quantities
Example: Police-to-population ratio
50 police : 10,000 people = 1:200
Proportion:
Equality of two ratios
a/b = c/d
Cross multiply: a × d = b × c
🎯 Practice Problem:
If 3 police officers can patrol 12 blocks, how many officers are needed for 28 blocks?
Solution
3/12 = x/28
12x = 3 × 28
12x = 84
x = 84 ÷ 12 = 7 officers
5. Crime Statistics & Data Interpretation 📊
Tol, numbers tell the story of crime trends!
Key Statistical Measures:
Mean (Average)
Sum of all values ÷ Number of values
Example: Average crimes per month
Median
Middle value when arranged in order
Example: Middle age of offenders
Mode
Most frequently occurring value
Example: Most common crime type
Range
Highest value - Lowest value
Example: Spread of response times
📈 Crime Rate Formula:
Crime Rate = (Number of Crimes ÷ Population) × 100,000
Example:
500 crimes in a city of 250,000 people
Rate = (500 ÷ 250,000) × 100,000 = 200 per 100,000
6. Work & Time Problems ⏰
Para sa task completion at resource planning!
Work Rate Formula:
Work = Rate × Time
Rate = 1/Time to complete the job
Example:
Officer A can complete a report in 3 hours.
Officer B can complete it in 6 hours.
How long if they work together?
Rate A = 1/3, Rate B = 1/6
Combined Rate = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
Time = 1 ÷ (1/2) = 2 hours
7. Age Problems 👤
Classic sa exams - mga computation ng edad!
🎯 Age Problem Tips:
- • Let x = present age (usually)
- • "Years ago" means subtract
- • "Years from now" means add
- • Set up equation based on relationship
Example:
Juan is 3 times as old as Pedro. In 10 years, Juan will be twice as old.
How old is Pedro now?
Solution
Let Pedro's age = x, Juan's age = 3x
In 10 years: 3x + 10 = 2(x + 10)
3x + 10 = 2x + 20
x = 10
Pedro is 10 years old
🎯 Quantitative Reasoning Exam Strategy
Tips for Success, Tol:
📝 During the Exam:
- • Read the problem twice
- • Identify what's being asked
- • Write down given information
- • Show your work (for checking)
⚡ Time-Saving Tips:
- • Estimate before computing
- • Use elimination method
- • Skip hard ones, return later
- • Double-check calculations
Numbers don't lie, Tol! Master the math, master the exam! 🔢💪
Test Your Knowledge! 🧠
Ready ka na ba? Take the practice quiz for Quantitative Reasoning to reinforce what you just learned.
Start Practice Quiz 📝