Mathematical Operations Practice Questions with Detailed Solutions – Level 3

Hard Mathematical Operations Questions for Reasoning: Level 3 Practice

Aspirants who have finished the basic and medium levels can use this set for advanced practice. Level 3 on Aptitude360 is a hard mathematical operations quiz. It covers multi-step sign substitution, letter-coded operations, combined interchanges of signs and numbers, and nested defined operations. A worked solution is given for every question.

What the Level 3 mathematical operations questions test

• Longer sign substitution expressions with many operations in a row
• Letter-coded signs such as P, Q, R and S, or G, H, J and K
• Interchanging two signs and two numbers together in one equation
• Picking the expression that equals a given value from several coded options
• Nested defined operations where one custom operation feeds into another
• Missing-number problems inside coded equations
• Completing an equation by choosing the right order of signs

Rules to apply in hard mathematical operations problems

• Order of operations: \( a-b\div c=a-\dfrac{b}{c} \)
• Square of a sum: \( (a+b)^{2}=a^{2}+2ab+b^{2} \)
• Square of a difference: \( (a-b)^{2}=a^{2}-2ab+b^{2} \)
• Nested operation: evaluate \( (a\ast b) \) first, then use it as the new input
• Left to right for equal priority: \( a\div b\div c=\dfrac{a}{bc} \)

Preparation tips for Level 3 coded operations

• When signs and numbers are both interchanged, swap the numbers first and then the signs, and write the new equation out
• Use the answer options to eliminate choices quickly in which-expression-equals questions
• Keep a written decode table for letter codes so you do not mix up similar letters
• Check whether a defined operation is symmetric before reusing a computed value

Who this hard level suits

This level suits learners in the final revision stage who already solve basic sign substitution easily and want tougher reasoning practice.