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SSC CGL Reasoning · Mathematical Operations

Symbol Substitution

Each 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.

All Mathematical Operations notes

Why this matters

Sixty-four questions in the bank, 41 EASY and 23 MODERATE, and 54 of them come from the 2025 shifts. The meanings arrive as other signs, as words or as letters, and a mark is usually lost to one sign rewritten wrong, not to the arithmetic.

Concept 1 of 4: Work the row in BODMAS order

SSC prints the expression in one line, but you cannot work it from left to right. Brackets go first, then division and multiplication, then addition and subtraction.

Definition

  • Brackets first, the innermost pair first.
  • Powers next: 525^2 is 25.
  • Division and multiplication are one level. Work them as they come, from left to right: 24÷4×2=6×2=1224 \div 4 \times 2 = 6 \times 2 = 12.
  • Addition and subtraction are the lowest level, again from left to right.
  • A negative number in brackets, such as (−6)(-6), is one number. Subtracting it adds 6.
  • Quick check: when every option is a whole number and your answer is not, look for a slip before you move on.

Order of operations

Brackets→Powers→(÷ and ×)→(+ and −)\text{Brackets} \to \text{Powers} \to (\div \text{ and } \times) \to (+ \text{ and } -)

Worked example

Work out 48÷6×2+15−3×448 \div 6 \times 2 + 15 - 3 \times 4.
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 3 · Q8Moderate

Example 1 · Mathematical Operations · Symbol Substitution

If 'P' denotes 'addition', 'D' denotes 'subtraction', 'S' denotes 'multiplication', and 'V' denotes 'division', then what will be the value of the following expression? {20 D (25 D 33)} V {−5 S 4 D (−6)} P 56 V (−27 P 13)\{20\ \text{D}\ (25\ \text{D}\ 33)\}\ \text{V}\ \{-5\ \text{S}\ 4\ \text{D}\ (-6)\}\ \text{P}\ 56\ \text{V}\ (-27\ \text{P}\ 13)

Always multiplying before dividing

Division and multiplication share one level. 24÷4×224 \div 4 \times 2 is 6×2=126 \times 2 = 12, worked from the left. Doing the multiplication first gives 24÷8=324 \div 8 = 3, which is wrong.

Always adding before subtracting

Addition and subtraction also share one level. 20−8+220 - 8 + 2 is 12+2=1412 + 2 = 14, not 20−10=1020 - 10 = 10.
Drill 5 more on work the row in bodmas order

Concept 2 of 4: Signs that stand for other signs

When ‘+’ means ‘×’ and ‘×’ means ‘−’, every sign in the row changes at the same moment. Copy the row once with the new signs, reading each sign from the printed row, and only then calculate.

Definition

  • Write the key first, for example: + becomes ×, − becomes ÷, × becomes +, ÷ becomes −.
  • Go along the printed row and write the new sign under each old one. Each printed sign changes once.
  • Meanings in words work the same way: subtraction is −, addition is +, multiplication is ×, division is ÷.
  • The letter x may be given its own meaning, such as ‘minus’. Then the x in the row is a minus sign, not a times sign.
  • A sign the stem does not mention keeps its usual meaning.
  • Then work out the new row in BODMAS order.
  • Fast route: after rewriting, work out the division and multiplication blocks first. The options are usually far apart, so the blocks alone often show which option the total must be.

Worked example

If ‘+’ means ‘÷’, ‘−’ means ‘+’, ‘×’ means ‘−’ and ‘÷’ means ‘×’, what is the value of 72+8÷3−15×672 + 8 \div 3 - 15 \times 6?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 1 · Q24Easy

Example 2 · Mathematical Operations · Symbol Substitution

If '+' means '×\times', '-' means '÷\div', '×\times' means '+', then 4−2×3+6=?4 - 2 \times 3 + 6 = ?

Changing a sign twice

With + becoming × and × becoming +, a student who rewrites + as × and then reads that new × as + has undone the change. Read every sign from the printed row, never from your rewritten one.

Reading the letter x as times

When the stem says ‘x’ means ‘minus’, the x in the expression is a minus sign. Only the printed × sign, if the stem gives it a meaning, follows that meaning.
Drill 34 more on signs that stand for other signs

Concept 3 of 4: Letters and symbols in place of signs

Here the row has no signs at all, only letters such as P and Q or marks such as # and @. Turn each one into its sign and you have an ordinary sum.

Definition

  • Write the key, for example P is +, Q is ×, R is −, S is ÷.
  • Rewrite the row with real signs. The numbers stay where they are.
  • If the meanings are given in words (‘P denotes addition’), turn the words into signs first.
  • Then work it out in BODMAS order, brackets first.

Worked example

If ‘A’ means ‘×’, ‘B’ means ‘+’, ‘C’ means ‘÷’ and ‘D’ means ‘−’, find the value of 14 A 3 B 56 C 8 D 5.
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 3 · Q23Easy

Example 3 · Mathematical Operations · Symbol Substitution

If 'A' means '−-', 'B' means '÷\div', 'C' means '++', and 'D' means ‘×\times’ what is the value of the following expression? 25 B 5 C 3 D 2 A 4=?

Working the letters from left to right

Once the letters are signs, BODMAS still applies. If P is + and Q is ×, then 6 P 4 Q 5 is 6+20=266 + 20 = 26, not 10×5=5010 \times 5 = 50.
Drill 11 more on letters and symbols in place of signs

Concept 4 of 4: Which equation is correct?

Now the meanings are given and four whole equations are offered. Rewrite each option with the real signs, work it out, and keep the one whose two sides agree.

Definition

  • Apply the key to every sign in the option, on both sides of the = sign. The numbers do not change.
  • Work out each side in BODMAS order.
  • Fast route: start with options whose rewritten row divides cleanly. A division that leaves a fraction no later step clears cannot reach a whole-number right side.
  • When all four options share one left side and only the right side differs, work out the left side once and pick the matching number.

Worked example

If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’ and ‘÷’ means ‘+’, which equation is correct? (a) 20+4−3÷6=1420 + 4 - 3 \div 6 = 14 (b) 18×3−2+5=918 \times 3 - 2 + 5 = 9 (c) 9−4×6÷1=89 - 4 \times 6 \div 1 = 8
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 1 · Q22Moderate

Example 4 · Mathematical Operations · Symbol Substitution

If '×\times' = '+', '+' = '-', '-' = '÷\div', '÷\div' = '×\times', which equation is correct?

Stopping at a near miss

SSC prints options that come close. A left side of 10.5 against a right side of 10 is wrong, so finish the arithmetic before you choose.

Rewriting only the left side

The key applies to every sign in the option. If a sign stands on the right of the = sign, it changes too.
Drill 10 more on which equation is correct?

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

  • Work the row in BODMAS order

    Order of operations

    Brackets→Powers→(÷ and ×)→(+ and −)\text{Brackets} \to \text{Powers} \to (\div \text{ and } \times) \to (+ \text{ and } -)

Watch out for (7)

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.

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