SSC CGL Reasoning · Free notes
Mathematical Operations: SSC CGL Reasoning
Mathematical Operations has 282 questions in the SSC CGL Tier I bank: 80 from the 2023 shifts, 79 from the 2024 shifts and 123 from the 2025 shifts. None is HARD and 171 are EASY, so this chapter rewards care and speed: Tier I gives you about 36 seconds a question. Nearly every question rests on two habits. Rewrite each sign exactly as the stem says, reading from the printed row, and then work out the row in BODMAS order. The fast routes on these pages remove wrong options before you calculate, and each one says when it is safe to use.
The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.
Subtopic notes
Symbol Substitution
64 PYQsEach sign, word or letter in the row is given a new meaning. Rewrite the whole row with the real signs first, then work it out in BODMAS order.
Value After Interchanging Signs
57 PYQsWhen two signs are interchanged, each takes the other's place everywhere in the row. Make both swaps at once, then work out the new row in BODMAS order.
Signs to Balance an Equation
36 PYQsThe signs are missing from a row of numbers. Put each option's signs into the gaps in order and keep the one that makes both sides equal.
Interchanging Two Signs
42 PYQsThe equation is wrong as printed. Swap the two signs an option names, everywhere they appear, and keep the option that makes both sides equal.
Interchanging Signs and Numbers
27 PYQsHere numbers move as well as signs. Put each option's two numbers in each other's places, swap its two signs too if it names any, and check the equation.
Hidden Operation Rules
56 PYQsA made-up symbol stands for a rule. Either the stem states the rule, or it shows worked examples and you find the rule, test it on every example, and only then use it.
Formula & revision sheet
3 formulas · 29 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
3 formulas · 29 gotchas across all subtopics — the exam-eve cheat-sheet
Watch out for (7)
- Always multiplying before dividing→ Work the row in BODMAS order
- Always adding before subtracting→ Work the row in BODMAS order
- Changing a sign twice→ Signs that stand for other signs
- Reading the letter x as times→ Signs that stand for other signs
- Working the letters from left to right→ Letters and symbols in place of signs
- Stopping at a near miss→ Which equation is correct?
- Rewriting only the left side→ Which equation is correct?
Watch out for (4)
- Swapping in one direction only→ Plus with minus, times with divide
- Changing the order inside a block→ Plus with minus, times with divide
- Keeping the old products→ Swaps across the levels
- Treating a one-way list as swaps→ Swaps across the levels
Watch out for (4)
- Filling the gaps out of order→ Filling the gaps when the = sign is fixed
- Calling a fraction a dead end too early→ Filling the gaps when the = sign is fixed
- Carrying a sign across the = sign→ When the = sign is one of the signs to place
- Assuming the last number is the right side→ When the = sign is one of the signs to place
Watch out for (4)
- Swapping only one of two signs→ Swapping plus with minus, or times with divide
- Using the 2(m − p) check on a longer row→ Swapping plus with minus, or times with divide
- Ruling out a fraction too early→ Swaps that change what is done first
- Choosing on size alone→ Swaps that change what is done first
Watch out for (4)
- Swapping digits→ Swapping two numbers
- Forgetting the right side can move→ Swapping two numbers
- Making only one of the two moves→ Swapping two numbers and two signs
- Moving the brackets→ A stated swap applied to four equations
Watch out for (6)
- Putting the numbers in the wrong places→ A rule you are given
- Stopping after one example→ Finding the rule from examples
- Missing a second rule that fits→ Finding the rule from examples
- Settling for a rule that fits two→ The odd one out among four results
- Checking only the first step→ Chains of operations on number sets
- Splitting a number into digits→ Chains of operations on number sets
PYQ weightage by concept
17 concepts · 282 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
17 concepts · 282 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Signs that stand for other signs | 35 | 12% |
| Letters and symbols in place of signs | 12 | 4% |
| Which equation is correct? | 11 | 4% |
| Work the row in BODMAS order | 6 | 2% |
| Concept | PYQs | Share |
|---|---|---|
| Plus with minus, times with divide | 45 | 16% |
| Swaps across the levels | 12 | 4% |
| Concept | PYQs | Share |
|---|---|---|
| Filling the gaps when the = sign is fixed | 28 | 10% |
| When the = sign is one of the signs to place | 8 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Swaps that change what is done first | 26 | 9% |
| Swapping plus with minus, or times with divide | 16 | 6% |
| Concept | PYQs | Share |
|---|---|---|
| Swapping two numbers and two signs | 14 | 5% |
| Swapping two numbers | 10 | 4% |
| A stated swap applied to four equations | 3 | 1% |
| Concept | PYQs | Share |
|---|---|---|
| Finding the rule from examples | 41 | 15% |
| Chains of operations on number sets | 7 | 2% |
| A rule you are given | 5 | 2% |
| The odd one out among four results | 3 | 1% |
Test yourself on Mathematical Operations
20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.