ASVAB Section 6 : Mathematics Knowledge UPDATED SOLUTION 2023

ASVAB Section 6 : Mathematics
Knowledge UPDATED SOLUTION 2023



Question 1 — Order of Operations

Evaluate:
26 − 7(3 + 5) ÷ 4 + 2

A) 14
B) 16.67
C) 23
D) 40

Answer: A) 14
Rationale: Follow PEMDAS:

1. Parentheses: (3+5)=8
2. Then multiply and divide: 7×8=56, 56÷4=14
3. Now left with: 26 − 14 + 2 = 14



Question 2 — Exponent Rules

Simplify: (x⁶)(x⁵)
A) 2x¹¹ B) 2x³⁰ C) x¹¹ D) x³⁰

Answer: C) x¹¹
Rationale: When multiplying like bases, add exponents: x⁶ * x⁵ = x^(6+5) = x¹¹

, Question 3 — Solving an Equation

Solve: 3(x + 1) = 5(x − 2) + 7
A) −2 B) 2 C) ½ D) 3

Answer: D) 3
Rationale:
3x+3 = 5x−10+7 → 3x+3 = 5x−3 → 3+3 = 5x−3x → 6 = 2x → x = 3



Question 4 — Evaluate an Expression

If y = 3ab + 2b³, a=1, b=2, find y.
A) 16 B) 18 C) 20 D) 22

Answer: D) 22
Rationale:
y = 3(1)(2) + 2(2³) = 6 + 2(8) = 6 + 16 = 22



Question 5 — Percentage

44 is 80% of what number?
A) 51 B) 53 C) 55 D) 57

Answer: C) 55
Rationale: Translate to equation:
44 = 0.8x → x = 44 ÷ 0.8 = 55



Question 6 — Geometry

Area of a triangle: base = 6 cm, height = 8 cm.
A) 14 cm² B) 24 cm² C) 28 cm² D) 48 cm²

Answer: B) 24 cm²
Rationale: Area = ½ × base × height = ½ × 6 × 8 = 24