NMAT Quantitative Reasoning
Complete guide to Math Concepts, Data Analysis & Problem Solving
In This Lesson
Arithmetic & Number Sense
Fractions, Decimals, Percentages
Quick Conversions
Fraction → Decimal
Divide: 3/4 = 0.75
Decimal → Percent
Multiply by 100: 0.75 = 75%
Percent → Fraction
Divide by 100: 75% = 75/100 = 3/4
Common Fractions to Memorize
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
Ratio and Proportion
Key Concepts
- Ratio: Comparison of two quantities (e.g., 3:2 or 3/2)
- Proportion: Two equal ratios (a/b = c/d)
- Cross-multiply: ad = bc
- Direct Proportion: As x increases, y increases proportionally
- Inverse Proportion: As x increases, y decreases proportionally
Order of Operations (PEMDAS)
P - Parentheses
E - Exponents
M/D - Multiplication/Division (left to right)
A/S - Addition/Subtraction (left to right)
Algebra
Linear Equations
Solving Linear Equations
One variable: 2x + 5 = 11 → 2x = 6 → x = 3
Two variables (system):
Substitution: Solve one equation for a variable, substitute into other
Elimination: Add/subtract equations to eliminate a variable
Quadratic Equations
Standard Form: ax² + bx + c = 0
Quadratic Formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant (b² - 4ac):
- > 0: Two real solutions
- = 0: One real solution
- < 0: No real solutions
Exponents and Radicals
Exponent Rules
- a^m × a^n = a^(m+n)
- a^m ÷ a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1
- a^(-n) = 1/a^n
Radical Rules
- √(ab) = √a × √b
- √(a/b) = √a / √b
- √a² = |a|
- a^(1/n) = ⁿ√a
Factoring
- Common Factor: ab + ac = a(b + c)
- Difference of Squares: a² - b² = (a+b)(a-b)
- Perfect Square Trinomial: a² ± 2ab + b² = (a ± b)²
- General Trinomial: x² + bx + c = (x + p)(x + q) where p + q = b and pq = c
Geometry
Basic Shapes - Area and Perimeter
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | A = lw | P = 2l + 2w |
| Square | A = s² | P = 4s |
| Triangle | A = ½bh | P = a + b + c |
| Circle | A = πr² | C = 2πr |
| Trapezoid | A = ½(b₁+b₂)h | P = a+b+c+d |
3D Shapes - Volume and Surface Area
Rectangular Prism (Box)
V = lwh
SA = 2(lw + lh + wh)
Cylinder
V = πr²h
SA = 2πr² + 2πrh
Sphere
V = (4/3)πr³
SA = 4πr²
Cone
V = (1/3)πr²h
SA = πr² + πrl
Pythagorean Theorem
a² + b² = c²
For right triangles: c is the hypotenuse (longest side)
Common Pythagorean Triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25
Coordinate Geometry
- Distance: d = √[(x₂-x₁)² + (y₂-y₁)²]
- Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)
- Slope: m = (y₂-y₁)/(x₂-x₁)
- Slope-Intercept Form: y = mx + b
Data Analysis & Statistics
Measures of Central Tendency
Mean (Average)
Sum of all values divided by count
x̄ = Σx / n
Median
Middle value when data is ordered
If even count: average of two middle values
Mode
Most frequently occurring value
Can have multiple modes
Measures of Spread
- Range: Maximum - Minimum
- Variance: Average of squared deviations from mean
- Standard Deviation: Square root of variance (measures spread around mean)
Probability
Basic Probability
P(event) = favorable outcomes / total outcomes
- • P(A and B) = P(A) × P(B) if independent
- • P(A or B) = P(A) + P(B) - P(A and B)
- • P(not A) = 1 - P(A)
Reading Charts & Graphs
Graph Types
- • Bar graphs: Compare categories
- • Line graphs: Show trends over time
- • Pie charts: Show parts of a whole
- • Scatter plots: Show relationships
Tips for Analysis
- • Read axis labels carefully
- • Note the scale/units
- • Look for trends and patterns
- • Watch for misleading graphs
Problem-Solving Strategies
NMAT Quantitative Tips
- Read carefully: Identify what is being asked
- Translate to math: Convert words to equations
- Estimate first: Eliminate obviously wrong answers
- Work backwards: Start from answer choices if easier
- Pick numbers: Substitute simple values to test
- Draw diagrams: Visualize geometry problems
- Check units: Ensure consistency (hours, minutes, etc.)
- Manage time: Don't spend too long on one problem
Common Word Problem Types
Rate/Speed Problems
Distance = Rate × Time
Example: If a car travels at 60 km/h for 2.5 hours, how far does it go?
Work Problems
1/t₁ + 1/t₂ = 1/t_total
Example: If A can do a job in 3 hours and B in 6 hours, how long together?
Percentage Problems
Part = Percent × Whole
Example: What is 15% of 200? → 0.15 × 200 = 30
Age Problems
Set up equations using present age and years ago/from now
Example: Ana is twice as old as Ben. In 5 years, their ages will sum to 40.
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