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Mathematical Operations Practice Questions with Detailed Solutions – Level 2

Medium-level mathematical operations practice on sign substitution, letter and word codes, sign and number interchanges, and defined operations, with a worked solution for every question.

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Questions, answer key and solutions.

Questions
50
Duration
50 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 50-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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How the two modes differ
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Normal

Untimed

Every question on one page, loading as you scroll. Choose an option and see straight away whether it was right.

  • No timer. Nothing to start and nothing to submit. Stop whenever you like.
  • Answered as you choose. Tap an option and it is marked at once, with the correct answer shown.
  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
  • Open to guests. Normal practice needs no sign-in.
Real exam conditions

Simulated

Timed CBT

The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 50 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
  • Question palette. Answered, not answered and marked for review, section by section, as the real interface has it.
  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
  • Answers hidden until you submit. The key, the explanations and your score all arrive together at the end.

About this test

Mathematical Operations Reasoning Practice Quiz Level 2 with Solutions

This is the Level 2 Mathematical Operations practice set on Aptitude360. It is a reasoning quiz where you replace symbols, letters or words with arithmetic signs and then evaluate the result. It also covers interchanging signs and numbers to balance equations and working out custom-defined operations.

Topics covered in this Mathematical Operations Level 2 set

  • Sign substitution, where one arithmetic sign stands for another
  • Letter-coded signs such as P, Q, R and S, or A, B, C and D, standing for the four operations
  • Word-coded operations, where words like plus and minus are swapped
  • Interchanging two signs or two numbers to make an equation correct
  • Choosing the correct sequence of signs to balance an equation
  • Defined operations using symbols like star, diamond and circled plus, including nested expressions
  • Finding the missing number in a coded equation
  • Spotting the pattern behind a hash-type number rule

Key BODMAS rules for mathematical operations questions

  • Division and multiplication before addition and subtraction: \( a+b\times c=a+(b\times c) \)
  • Distributing over a bracket: \( (a+b)\times c=ac+bc \)
  • Powers before multiplication: \( a\times b^{2}=a\times(b\times b) \)
  • Equal priority works left to right: \( a\div b\times c=\dfrac{a}{b}\times c \)
  • Subtraction is not commutative in general: \( a-b\neq b-a \) when \( a\neq b \)

Revision tips for coded sign questions

  • Rewrite the whole expression with the real signs before you calculate anything
  • Apply BODMAS only after decoding, never on the coded symbols
  • For defined operations, solve the inner bracket first and substitute its value carefully
  • In interchange questions, test each option by rewriting the equation in full

Who should take this Level 2 practice

Students who are comfortable with basic sign substitution and want medium-level practice for reasoning sections in competitive exams.

FAQs about Mathematical Operations Practice Questions with Detailed Solutions – Level 2

What is mathematical operations in reasoning?
It is a reasoning topic where arithmetic signs are replaced by other signs, letters, symbols or words. You decode the substitution and then evaluate or balance the expression using the usual order of operations.
Which rule is used to solve mathematical operations problems?
The BODMAS rule is used: brackets, orders or powers, division and multiplication, then addition and subtraction. Division and multiplication have equal priority and are worked left to right, and the same applies to addition and subtraction.
How do you solve interchanging signs problems?
Swap the two signs given in each option, rewrite the equation and calculate the left side using BODMAS. The correct option is the one where both sides become equal.
What is a defined operation in reasoning?
A defined operation is a new symbol, such as a star or circled plus, given its own rule in terms of ordinary arithmetic. You substitute the numbers into that rule exactly as stated, solving any inner bracket first.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Mathematical Operations Level 25050 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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