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Lesson 4 - 20% of Exam
Quantitative Reasoning
In This Lesson
1. Number Properties
Understanding number properties helps solve problems quickly.
Even and Odd Numbers
Addition:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
Multiplication:
- Even × Even = Even
- Odd × Odd = Odd
- Even × Odd = Even
Divisibility Rules
By 2: Last digit is even
By 3: Sum of digits divisible by 3
By 4: Last two digits divisible by 4
By 5: Last digit is 0 or 5
By 6: Divisible by both 2 and 3
By 9: Sum of digits divisible by 9
By 10: Last digit is 0
Prime Numbers
Divisible only by 1 and itself.
First 15 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Note: 2 is the only even prime number.
2. Percentages & Ratios
Percentage Formulas
- Basic: Percentage = (Part/Whole) × 100
- Finding Part: Part = (Percentage/100) × Whole
- Percent Change: ((New - Old)/Old) × 100
- Percent Increase: Original × (1 + rate)
- Percent Decrease: Original × (1 - rate)
Common Conversions
25% = 1/4
50% = 1/2
75% = 3/4
20% = 1/5
33.3% = 1/3
66.7% = 2/3
10% = 1/10
12.5% = 1/8
40% = 2/5
Ratios and Proportions
- Ratio: Comparison of two quantities (a:b or a/b)
- Proportion: Two equal ratios (a:b = c:d)
- Cross-multiply: If a/b = c/d, then ad = bc
- Part to Whole: If ratio is 2:3, parts are 2/5 and 3/5 of total
3. Statistics
Measures of Central Tendency
Mean
Sum ÷ Count
(Average)
Median
Middle value
(When sorted)
Mode
Most frequent
(Can have none or multiple)
Other Measures
- Range: Maximum - Minimum
- Weighted Average: Σ(value × weight) ÷ Σweights
Example
Data set: 3, 5, 7, 7, 9
- Mean: (3+5+7+7+9)/5 = 31/5 = 6.2
- Median: 7 (middle value)
- Mode: 7 (appears most often)
- Range: 9 - 3 = 6
4. Data Interpretation
Understanding graphs, charts, and tables is essential for the PhiLSAT.
Chart Types
- Bar Charts: Compare quantities across categories
- Line Graphs: Show trends over time
- Pie Charts: Show parts of a whole (percentages add to 100%)
- Tables: Present precise numerical data
Reading Data Tips
- Read the title and labels carefully
- Note the units and scale
- Look for trends and patterns
- Compare values accurately
- Be careful with different scales on axes
- Watch for missing data or gaps
5. Word Problems
Translate words into mathematical expressions.
Problem-Solving Steps
- Read carefully - identify what is being asked
- Identify given information and unknowns
- Translate words to equations
- Solve the equation
- Check if the answer makes sense
Common Formulas
- Distance: Distance = Speed × Time
- Work: Work = Rate × Time
- Combined Work: 1/Total Time = 1/Time₁ + 1/Time₂
- Simple Interest: I = P × R × T
Example Problem
If a lawyer charges ₱5,000 per hour and worked for 3.5 hours on a case, with a 20% discount for the client, what is the total fee?
- Original fee: ₱5,000 × 3.5 = ₱17,500
- Discount: ₱17,500 × 0.20 = ₱3,500
- Final fee: ₱17,500 - ₱3,500 = ₱14,000
PhiLSAT Quantitative Tips
- ✓Memorize common conversions - fractions, decimals, percentages.
- ✓Practice mental math - speed matters on the exam.
- ✓Read graphs carefully - note units and scales.
- ✓Estimate first - eliminate obviously wrong answers.
Congratulations!
You've completed all PhiLSAT study notes. You're ready for law school admission!