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.
Full four-operator substitution
very commonThe question says 'If + means ×, − means ÷, × means +, ÷ means −' (or similar) and gives an expression.
How to solve: Write the mapping, rewrite the whole line converting each sign once, then apply BODMAS. The original value and the left-to-right value are always planted as wrong options.
Example: If + means ×, − means ÷, × means +, ÷ means −, find 6 + 2 × 4 ÷ 2 − 2.
Rewrite: 6 × 2 + 4 − 2 ÷ 2 = 12 + 4 − 1 = 15.
Letter-coded or partial substitution
commonLetters (A, B, C, D or P, Q, R, S) stand for signs, or only two signs change meaning.
How to solve: Replace each code by its real sign, leave the unlisted signs as they are, and calculate with BODMAS. Signs inside brackets are converted too.
Example: A means +, B means −, C means ×, D means ÷. Find 18 C 4 D 6 A 9 B 5.
18 × 4 ÷ 6 + 9 − 5 = 12 + 9 − 5 = 16.
Interchange signs or numbers, then evaluate
common'If + and × are interchanged (and 2 and 8 are interchanged), find the value of ...'.
How to solve: Interchange is a two-way swap. Do all swaps in one rewrite, change whole numbers only, then apply BODMAS.
Example: Interchange + and ×: find 3 × 4 + 5 − 6.
3 + 4 × 5 − 6 = 3 + 20 − 6 = 17.
Which two numbers or signs to interchange
commonA false equation is given; options are pairs like '2 and 3' or '+ and −'.
How to solve: Sweep the option pairs in a fixed order. Swap, evaluate the left side, and stop at the pair that equals the right side. Use target size and last digits to skip hopeless pairs.
Example: Which two numbers should be interchanged: 4 + 2 × 6 − 3 = 20?
Swap 2 and 3: 4 + 3 × 6 − 2 = 4 + 18 − 2 = 20 ✓ → 2 and 3.
Pick the correct equation
very commonFour complete equations are given and only one is arithmetically true.
How to solve: Evaluate every left side with BODMAS in writing and compare. Wrong options are usually built from left-to-right working, so careful BODMAS finds the answer fast.
Example: Which is correct: 7 + 8 × 2 − 5 = 25 or 16 ÷ 4 × 2 + 6 = 14?
7 + 16 − 5 = 18 ✗; 4 × 2 + 6 = 14 ✓ → 16 ÷ 4 × 2 + 6 = 14.
Sequentially replace the * signs
very common21 * 7 * 5 * 4 * 3 = 27 or 12 * 4 * 3 * 16 with options such as '÷, ×, +, ×' (sometimes including '=').
How to solve: Place the option's signs into the * marks from left to right and evaluate. If '=' is one of the signs, compare the two sides after filling.
Example: 21 * 7 * 5 * 4 * 3 = 27 — does '÷, ×, +, ×' work?
21 ÷ 7 × 5 + 4 × 3 = 15 + 12 = 27 ✓.
Fill the blanks with a sign pair or set
common'Which set of signs will make 18 ? 6 ? 3 ? 4 = 24 correct?'
How to solve: Test each option in order with BODMAS. A big right side needs ×; a small one needs ÷ or −.
Example: 18 ? 6 ? 3 ? 4 = 24 — test '−, +, ×'.
18 − 6 + 3 × 4 = 12 + 12 = 24 ✓.
Hidden rule from solved examples
occasionalTwo or three worked examples like 5 # 3 = 34, 6 # 2 = 40 are given and a new pair is asked.
How to solve: Try the common rules — a + b, ab, a² ± b², (a ± b)², ab + a + b — and keep only the rule that fits every example. Then apply it.
Example: 5 # 3 = 34, 6 # 2 = 40. Find 7 # 4.
a² + b² fits both examples: 49 + 16 = 65.
Defined symbol with a formula
occasional'If a ★ b = 2a + 3b ...' or a conditional/nested definition.
How to solve: Write a and b before plugging in; solve inner brackets first; re-check any condition at each step.
Example: If a ★ b = 2a + 3b, find 5 ★ 4.
2 × 5 + 3 × 4 = 22.
BODMAS value or missing number
commonA plain expression to evaluate, or an equation with one '?'.
How to solve: Do brackets, then ÷ and × left to right, then + and − left to right. For a missing number, undo the steps backwards and put the value back to check.
Example: 18 + 6 × ? − 4 = 38. Find ?
6 × ? = 24, so ? = 4.