ReasoningAbility.com

Mathematical Operations - Advanced Level: mathematical manipulation ADVANCED

Exam-focused holistic practice ★ worksheet: 20 advanced-level mathematical operations questions. Worksheet 23 of 30 targets mathematical manipulation. Build proficiency in operation puzzles, symbolic operations, arithmetic operations with detailed solutions. Ideal for advanced competitive exam preparation.

📝 Worksheet 23 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Mathematical Operations
Worksheet 23 of 30 (76% complete)

Question 1

If $ means ×, % means ÷, @ means +, # means -, then find the value of (8 $ 6) % 12 @ 4
Step 1: (8 × 6) = 48
Step 2: 48 ÷ 12 + 4 = 8
substitution, brackets

Question 2

If $ means ×, # means -, @ means +, % means ÷, then find the value of (4 # 14) % 7 $ 6
Step 1: (4 - 14) = -10
Step 2: -10 ÷ 7 × 6 = -8.58
substitution, brackets

Question 3

If $ means ×, # means -, @ means +, % means ÷, then find the value of 6 % 7 $ 11
Substitute symbols: 6 ÷ 7 × 11 = 9.459999999999999
substitution, basic

Question 4

Given # means -, % means ÷, $ means ×, @ means +, which symbols should be interchanged to make 4 # 13 % 6 $ 10 = 43?
The equation is already correct or no single interchange works
interchange, complex

Question 5

Simplify: 4 + (11 + (15 - 14) × 7)
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 5
bodmas, complex

Question 6

A value increases by 26% and then decreases by 10%. What is the net percentage change?
Step 1: increase by 26% → multiply by 1.26
Step 2: decrease by 10% → multiply by 0.9
Net change = 13.4%
percentage, reasoning

Question 7

If $ means -, # means ×, @ means +, find 3 @ (5 # 9) $ 8
Step 1: (5 × 9) = 45
Step 2: 3 + 45 - 8 = 40
bodmas, brackets

Question 8

A value decreases by 43% and then decreases by 42%. What is the net percentage change?
Step 1: decrease by 43% → multiply by 0.5700000000000001
Step 2: decrease by 42% → multiply by 0.5800000000000001
Net change = -66.9%
percentage, reasoning

Question 9

Given @ means +, # means -, % means ÷, $ means ×, which symbols should be interchanged to make 8 @ 15 # 11 $ 8 = 67?
The equation is already correct or no single interchange works
interchange, complex

Question 10

If % means ÷, $ means ×, @ means +, # means -, then find the value of 9 $ 10 @ 5
Substitute symbols: 9 × 10 + 5 = 95
substitution, basic

Question 11

If % means ÷, @ means +, $ means ×, # means -, then find the value of 15 # 20 $ 14
Substitute symbols: 15 - 20 × 14 = -265
substitution, basic

Question 12

If % means ÷, $ means ×, @ means +, # means -, then find the value of (11 # 12) @ 5 % 11
Step 1: (11 - 12) = -1
Step 2: -1 + 5 ÷ 11 = 0.36
substitution, brackets

Question 13

If @ means +, # means ×, $ means -, find 8 @ (11 # 12) $ 12
Step 1: (11 × 12) = 132
Step 2: 8 + 132 - 12 = 128
bodmas, brackets

Question 14

What operator should replace '?' to make 16 - 12 ? 14 = 75?
The correct operator is None because 16 - 12 None 14 = 75
operator, reasoning

Question 15

Find the missing number in the sequence: 3, 9, 27, ?, 243
The pattern: Each term is multiplied by 3. Therefore, the missing number is 81
pattern, sequence

Question 16

A value decreases by 41% and then increases by 27%. What is the net percentage change?
Step 1: decrease by 41% → multiply by 0.5900000000000001
Step 2: increase by 27% → multiply by 1.27
Net change = -25.1%
percentage, reasoning

Question 17

Find the missing number in the sequence: 4, 12, 36, 108, ?, 972
The pattern: Each term is multiplied by 3. Therefore, the missing number is 324
pattern, sequence

Question 18

Simplify: 10 × (14 + (5 + 11) × 3)
Apply BODMAS: brackets first, then multiplication/division, then addition/subtraction to get 26
bodmas, complex

Question 19

If $ means ×, # means -, % means ÷, @ means +, then find the value of 3 % 5 @ 19
Substitute symbols: 3 ÷ 5 + 19 = 19.6
substitution, basic

Question 20

What operator should replace '?' to make 6 ? 5 + 17 = 20?
The correct operator is None because 6 None 5 + 17 = 20
operator, reasoning
Previous Worksheet Next Worksheet