Ch2. GMAT Quantitative Reasoning — Core Formulas & Problem Types

Quantitative Reasoning Overview

GMAT Focus Edition Quantitative Reasoning: 21 questions, 45 minutes. No calculator. Tests mathematical reasoning, not advanced math.

Question type: Problem Solving (5-choice multiple choice only)

1. Arithmetic

Primes & Divisibility

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29… (2 is the only even prime)
GMAT favorites: prime factorization, GCD (HCF), LCM

Percentages & Ratios

% change: (New − Old) / Old × 100
Weighted average: crucial for mixture problems

Number Properties

Even ± Even = Even; Odd ± Odd = Even; Even ± Odd = Odd
Even × anything = Even; Odd × Odd = Odd

2. Algebra

Quadratic Equations

ax² + bx + c = 0

Quadratic formula: x = [−b ± √(b²−4ac)] / 2a

Discriminant D = b²−4ac:

D > 0: two distinct real roots
D = 0: one repeated real root
D < 0: no real roots

Inequalities — Critical Rule

Multiplying or dividing by a negative number REVERSES the inequality sign. This is the #1 GMAT trap on inequality questions.

Absolute Value

|x| = k → x = k or x = −k

3. Geometry

Shape	Area	Perimeter
Square	s²	4s
Rectangle	lw	2(l+w)
Triangle	½bh	a+b+c
Circle	πr²	2πr
Trapezoid	½(a+b)h	—

Pythagorean theorem: a² + b² = c²

Special triangles:

30-60-90: sides in ratio 1 : √3 : 2
45-45-90: sides in ratio 1 : 1 : √2

4. Statistics

Mean: ∑x / n
Median: middle value when sorted
Mode: most frequent value
Range: max − min
Standard deviation: conceptual understanding > formula memorization

5. Probability & Combinatorics

Basic probability: P(A) = favorable outcomes / total outcomes

Addition rule: P(A∪B) = P(A) + P(B) − P(A∩B)

Independent events: P(A∩B) = P(A) × P(B)

Permutations: nPr = n! / (n−r)!

Combinations: nCr = n! / [r! × (n−r)!]

Time-Saving Strategies

Estimation

For answer choices spread far apart, estimate rather than calculate precisely.

Backsolving

Substitute answer choices (start with C, then adjust) into the problem to find the correct one — fastest when the answer choices are specific numbers.

Smart Algebra

Convert wordy problems to equations immediately. Assign variables and write equations before solving.

10-Question Practice

Q1. The sum of three consecutive integers is 57. What is the largest? A) 18 B) 19 C) 20 D) 21 E) 22

Q2. $240 is what percent of$ 300? A) 70% B) 75% C) 80% D) 85% E) 90%

Q3. A right triangle has legs 5 and 12. What is the hypotenuse? A) 11 B) 12 C) 13 D) 14 E) 15

Q4. How many ways can 2 people be chosen from a group of 5? A) 8 B) 10 C) 15 D) 20 E) 25

Q5. If n is even and m is odd, which is ALWAYS odd? A) n+m B) n×m C) n²+m D) 2n+m E) nm²

Answers: Q1:C, Q2:C, Q3:C, Q4:B, Q5:D

Chapter 3 Preview

Next: Verbal Reasoning — Critical Reasoning argument analysis (assumption, strengthen, weaken, inference) and Reading Comprehension speed strategies.