Mathematical Operations for the Assam Police Constable (AB & UB) Exam
Mathematical Operations is a reasoning topic of the SLPRB Assam Police Constable (AB & UB) examination in which a mathematical expression is given with the symbols replaced by new symbols or with the ordinary symbols interchanged, and the candidate must find the value of the expression. The topic needs no general knowledge and only simple arithmetic, and it rests on one fixed rule: replace the symbols, keep the order of operations, and then calculate. A candidate who writes the new expression before calculating almost never makes a mistake. This page explains the rules, the worked examples, the shortcuts and the traps that cost marks. The material follows the standard reasoning reference books used for Assam recruitment examinations and is reviewed before it is published.
What the Topic Means
In this topic a question gives either a set of substituted symbols, such as A for plus, B for minus, C for multiplication and D for division, or an interchange of the ordinary symbols, such as plus meaning multiplication. The candidate must rewrite the expression with the real symbols and then simplify it, taking care to follow the correct order of operations. In some questions a number is also given as the value of a symbol, and the candidate must substitute and simplify.
The Standard Rules
- Replace every given symbol with the operation it stands for before doing any calculation.
- Follow the order of operations: division and multiplication first, then addition and subtraction.
- Solve the brackets first, from the innermost to the outermost.
- When comparing two expressions, simplify both sides and then use the relation signs.
- When a symbol has a value, substitute the value and simplify.
A Step by Step Method
- Read the substitution carefully and note which symbol means which operation.
- Rewrite the expression in the ordinary symbols.
- Apply the order of operations and solve the brackets first.
- Simplify step by step and keep the working neat.
- Check the answer by substituting back.
Worked Examples
Example one: if A means plus and B means minus, then 4 A 5 B 3 equals 4 plus 5 minus 3, that is 6. Example two: if plus means multiplication and minus means division, then 8 plus 4 minus 2 equals 8 times 4 divided by 2, that is 16. Example three: if C means multiplication, then 3 C 4 plus 2 equals 12 plus 2, that is 14. Example four: if the value of A is 2, then 3 A plus 4 equals 3 times 2 plus 4, that is 10.
How This Topic Appears in the Examination
The topic usually appears as two to four objective questions of one mark each. The common forms are to substitute symbols and find the value, to interchange the ordinary symbols, to compare two expressions, and to solve a word problem in which each letter stands for a number. The questions are quick because they use one rule each.
Shortcuts and Speed Methods
- Rewrite the whole expression in the real symbols before calculating.
- Always follow the order of operations to avoid the classic error.
- Do the brackets first and simplify one line at a time.
- For comparison questions, reduce both sides to a single number.
- Check the answer by substituting back into the original expression.
Common Mistakes to Avoid
- Calculating from left to right and ignoring the order of operations.
- Forgetting to change every occurrence of a symbol.
- Reversing the meaning of a symbol, such as reading plus as minus.
- Solving the brackets after the other operations.
- Substituting the value of a symbol in the wrong place.
Preparation Plan
- Learn the order of operations by heart.
- Practise twenty substitution questions a day.
- Solve interchange and comparison questions separately.
- Check every answer by substituting back.
- Revise the rules once a week.
More Practice Questions
- If A means plus, then 7 A 8 equals 15.
- If plus means multiplication, then 6 plus 5 equals 30.
- If B means division, then 20 B 4 equals 5.
- If multiplication means subtraction, then 9 multiplication 4 equals 5.
- If the value of A is 3, then 2 A plus 1 equals 7.
Quick Revision Checklist
- Replace the symbols first, calculate afterwards.
- Division and multiplication before addition and subtraction.
- Brackets first, from the inside out.
- In comparisons, simplify both sides to a number.
- Always check by substituting back.
Frequently Asked Questions
What is the mathematical operations topic?
It is a reasoning topic in which a mathematical expression has its symbols replaced or interchanged, and the candidate must substitute the real symbols and find the value of the expression.
What is the main rule here?
Replace every symbol with the operation it stands for and then follow the order of operations, doing division and multiplication before addition and subtraction.
Why is the order of operations important?
If the expression is calculated from left to right the answer is wrong; the order of operations makes sure that division, multiplication, addition and subtraction are done in the correct sequence.
How do I solve comparison questions?
Substitute the symbols on both sides, simplify each side to a single number, and then place the correct relation sign between the two numbers.
Is mathematical operations scoring in Assam Police?
Yes. Each question uses one rule and can be solved in a few seconds, so it is a good place to gain sure marks in the reasoning paper.