Mathematical Operations
🔒 Log in to trackOperator-substitution puzzles: signs are redefined or interchanged, equations must be balanced, and the correct equation picked from four. The arithmetic is primary-school level — marks are lost to BODMAS slips and half-applied substitutions, not to difficulty. A disciplined rewrite-then-evaluate habit makes this one of the safest scoring topics in the paper.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
70 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (70 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Swap all four signs
very common"If + means ×, − means ÷, × means +, ÷ means −", followed by a sum.
Write what each sign means now.
Change every sign once, then solve with BODMAS.
If + means ×, − means ÷, × means +, ÷ means −, find 6 + 2 × 4 ÷ 2 − 2.
Change each sign: 6 × 2 + 4 − 2 ÷ 2
Do × and ÷ first: 12 + 4 − 1
Add and subtract: 15
Letters stand for signs
common"A means +, B means −, C means ×, D means ÷" and the sum is written with letters.
Put the real sign in place of each letter.
Then solve with BODMAS.
A means +, B means −, C means ×, D means ÷. Find 18 C 4 D 6 A 9 B 5.
Change letters: 18 × 4 ÷ 6 + 9 − 5
Do × and ÷ first: 72 ÷ 6 = 12
Then 12 + 9 − 5 = 16
Swap two signs, then solve
common"If + and × are interchanged, find the value of ..."
Swapping works both ways: every + becomes × and every × becomes +.
Change all of them at once, then use BODMAS.
If + and × are interchanged, find 3 × 4 + 5 − 6.
Swap the signs: 3 + 4 × 5 − 6
Do × first: 3 + 20 − 6
Then add and subtract: 17
Which two numbers to swap
commonA wrong equation is given and the options are pairs of numbers or signs.
Try each option pair: swap them and work out the left side.
Stop at the pair that gives the right side.
Which two numbers should be swapped to make 4 + 2 × 6 − 3 = 20 true?
Try swapping 2 and 3: 4 + 3 × 6 − 2
Do × first: 4 + 18 − 2
This is 20, so it works: 2 and 3
Pick the correct equation
very commonSeveral equations are given and only one of them is true.
Work out each left side with BODMAS.
Compare with the right side.
Which is correct: 7 + 8 × 2 − 5 = 25, or 16 ÷ 4 × 2 + 6 = 14?
First: 7 + 16 − 5 = 18, not 25
Second: 16 ÷ 4 = 4, then 4 × 2 = 8
8 + 6 = 14, which matches
Correct one: 16 ÷ 4 × 2 + 6 = 14
Put signs in place of *
very common"21 * 7 * 5 * 4 * 3 = 27" with options like "÷, ×, +, ×".
Put the option's signs into the * marks from left to right.
Solve with BODMAS and check the answer.
Do the signs ÷, ×, +, × make 21 * 7 * 5 * 4 * 3 = 27 true?
Fill in: 21 ÷ 7 × 5 + 4 × 3
Do ÷ and × first: 15 + 12
This is 27, so the answer is Yes
Choose the set of signs
common"Which set of signs makes 18 ? 6 ? 3 ? 4 = 24 correct?"
Test each option with BODMAS.
A big answer needs ×; a small one needs ÷ or −.
Test the signs −, +, × in 18 ? 6 ? 3 ? 4 = 24.
Fill in: 18 − 6 + 3 × 4
Do × first: 18 − 6 + 12
Then 12 + 12 = 24, so it works
Find the hidden rule
occasionalTwo or three solved examples like 5 # 3 = 34 are given, then a new pair.
Try simple rules like a + b, a × b, a² + b².
Keep the rule that fits every example, then use it.
If 5 # 3 = 34 and 6 # 2 = 40, find 7 # 4.
Try a² + b²: 25 + 9 = 34 ✓
Check: 36 + 4 = 40 ✓
So 7 # 4 = 49 + 16 = 65
Symbol with a given formula
occasional"If a ★ b = 2a + 3b, find 5 ★ 4."
Note which number is a and which is b.
Put the numbers into the formula.
If a ★ b = 2a + 3b, find 5 ★ 4.
Here a = 5 and b = 4
2 × 5 + 3 × 4 = 10 + 12
= 22
BODMAS sum or missing number
commonA plain sum to solve, or an equation with one ?.
Order: brackets, then × and ÷, then + and −.
For a missing number, work backwards.
18 + 6 × ? − 4 = 38. Find ?
Move numbers across: 6 × ? = 38 − 18 + 4
6 × ? = 24
? = 24 ÷ 6 = 4