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SSC CGL Reasoning · Mathematical Operations

Interchanging Signs and Numbers

Here 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.

All Mathematical Operations notes

Why this matters

Twenty-seven questions in the bank, every one MODERATE: ten swap two numbers only, fourteen swap two numbers and two signs, and three apply a stated swap to four equations. A division that must come out whole usually names the right pair before you calculate.

Concept 1 of 3: Swapping two numbers

The signs stay where they are and two numbers trade places. A number that ends up after a ÷ has to divide what comes before it, and that one fact rules out most options.

Definition

  • Swap whole numbers, never digits: 25 and 4 trade places, and 25 does not turn into 52.
  • Work out the printed left side first. The gap to the right side shows roughly how big the change must be.
  • If one of the two numbers is the right side, the target changes as well.
  • Fast route: after each swap, look at every ÷. If the divisor does not divide the number before it, and no later × clears the fraction, that option is out (when the target is a whole number).
  • Check the option that survives in full.

Worked example

Which two numbers should be interchanged to make 60÷3+5×6−12=1860 \div 3 + 5 \times 6 - 12 = 18 correct? (a) 3 and 6 (b) 5 and 12 (c) 60 and 12 (d) 3 and 5
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 10 Sep 2024, Shift 2 · Q10Moderate

Example 1 · Mathematical Operations · Interchanging Signs and Numbers

Which two numbers (not digits) should be interchanged to make the given equation correct? 116−92÷4+25×2−20=150116 - 92 \div 4 + 25 \times 2 - 20 = 150

Swapping digits

‘Numbers (not digits)’ means whole numbers trade places. 34 stays 34; it never becomes 43.

Forgetting the right side can move

When one of the two numbers is the one after the = sign, the swap changes the target too. Check the new left side against the new right side.
Drill 9 more on swapping two numbers

Concept 2 of 3: Swapping two numbers and two signs

Two moves at once: two numbers trade places and two signs trade places. The moves do not affect each other, so make both, then calculate.

Definition

  • Copy the row with the two numbers in each other's places, then swap the two signs in that copy. Doing the signs first gives the same row.
  • Work out the new row in BODMAS order.
  • Fast route: options often share the pair of signs or the pair of numbers. Find what differs between them and test that first.
  • A division in the new row that leaves a fraction no later step clears rules the option out when the target is whole.

Worked example

Which interchange makes 8+24÷3−6×4=208 + 24 \div 3 - 6 \times 4 = 20 correct? (a) 6 and 24, ÷ and × (b) 3 and 4, ÷ and × (c) 8 and 6, + and − (d) 24 and 4, − and ×
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 22 Sep 2025, Shift 3 · Q17Moderate

Example 2 · Mathematical Operations · Interchanging Signs and Numbers

Which interchanges of numbers and signs will make the equation correct? 7+3×4=197 + 3 \times 4 = 19

Making only one of the two moves

An option that names two numbers and two signs needs both swaps. Testing the numbers alone, or the signs alone, checks a different equation.
Drill 13 more on swapping two numbers and two signs

Concept 3 of 3: A stated swap applied to four equations

Here the stem names the swap, two signs and two numbers, and asks which equation holds after it. Apply that one swap to every option, then check each.

Definition

  • Apply the stated sign swap and the stated number swap to every option, on both sides.
  • Keep the brackets where they are; only the signs and numbers inside them change.
  • Work out each option and compare it with its right side.

Worked example

After interchanging − and ÷ and the numbers 2 and 6, which equation holds? (a) (12−6)÷2=4(12 - 6) \div 2 = 4 (b) (24−2)÷6=3(24 - 2) \div 6 = 3 (c) (18−2)÷6=1(18 - 2) \div 6 = 1 (d) (30−6)÷2=3(30 - 6) \div 2 = 3
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 3 · Q22Moderate

Example 3 · Mathematical Operations · Interchanging Signs and Numbers

After interchanging + & ×\times and 3 & 9, which of the following equations will hold true?

Moving the brackets

The brackets stay in place. After + and × are interchanged, (2+7)×3(2 + 7) \times 3 reads (2×7)+3=17(2 \times 7) + 3 = 17, not 2×(7+3)=202 \times (7 + 3) = 20.
Drill 2 more on a stated swap applied to four equations

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.

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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.

Take the Mathematical Operations chapter testDrill all 27 questions