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SSC CGL Reasoning · Mathematical Operations

Interchanging Two Signs

The equation is wrong as printed. Swap the two signs an option names, everywhere they appear, and keep the option that makes both sides equal.

All Mathematical Operations notes

Why this matters

Forty-two questions in the bank, 21 EASY and 21 MODERATE, asked in all three years. Each prints a wrong equation and four pairs of signs; a check of size, or of how far the value must move, usually leaves one pair to test in full.

Concept 1 of 2: Swapping plus with minus, or times with divide

Swapping + and − leaves every product and quotient as it was. Only the terms that were added are now taken away, and the other way round, so you can work out in advance how far the value will move.

Definition

  • First work out the printed left side and compare it with the right side. The gap tells you what the swap must do.
  • A term is what follows a + or − sign: a single number or a whole block such as 3×23 \times 2.
  • + and − swapped: the term after the + is now taken away and the term after the − is now added. With one of each, the value changes by twice (minus term less plus term).
  • × and ÷ swapped: the + and − stay; only the blocks change, so work out the new blocks.
  • Fast route: when the needed change equals 2(m−p)2(m - p), the + and − swap is the answer. It is safe only when the row has exactly one + and one −; with more, rewrite the row in full.

Swapping one plus and one minus

change in value=2 (m−p)\text{change in value} = 2\,(m - p)
  • mmthe term after the minus sign
  • ppthe term after the plus sign

Worked example

Which two signs should be interchanged to make 54÷6+11−3×2=454 \div 6 + 11 - 3 \times 2 = 4 correct? (a) + and − (b) ÷ and × (c) + and × (d) − and ÷
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 2 · Q8Moderate

Example 1 · Mathematical Operations · Interchanging Two Signs

Which two signs should be swapped to correct the following? 28÷4×3−5+7=1928 \div 4 \times 3 - 5 + 7 = 19

Swapping only one of two signs

If the row has two + signs, both become − when + and − are interchanged. Leaving one of them as + tests a different equation.

Using the 2(m − p) check on a longer row

The check needs exactly one + and one −. With two + signs, each of their terms is now subtracted, so the change is not 2(m−p)2(m - p); rewrite the row and work it out.
Drill 15 more on swapping plus with minus, or times with divide

Concept 2 of 2: Swaps that change what is done first

When a swap moves a sign across the levels (+ with ×, − with ÷, + with ÷), the blocks change and so does the size of the answer. A quick look at size throws out most wrong pairs before any arithmetic.

Definition

  • Compare the target with the printed left side. Much smaller, or much bigger?
  • If the printed row multiplies two large numbers and the target is small, the × must be one of the swapped signs. If a large number is meant to be divided down, the sign next to it must become ÷.
  • Whole-number check: after the swap, a ÷ must leave a whole number, or a fraction that a later × clears. If neither, and the target is whole, rule the pair out.
  • Test the pairs that survive in full, by BODMAS.

Worked example

Which two signs should be interchanged to make 18×15+3−9=5418 \times 15 + 3 - 9 = 54 correct? (a) + and − (b) × and + (c) × and −
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 1 · Q8Moderate

Example 2 · Mathematical Operations · Interchanging Two Signs

Which two signs should be interchanged to make the given equation CORRECT? 97×23−18+9÷3=6697 \times 23 - 18 + 9 \div 3 = 66

Ruling out a fraction too early

9÷69 \div 6 is 1.5, but 9÷6×4=69 \div 6 \times 4 = 6. Finish the whole block before you say a swap cannot give a whole number.

Choosing on size alone

A size check removes pairs; it does not prove one. Two pairs can both give an answer of about the right size, so work the last one out in full.
Drill 25 more on swaps that change what is done first

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)

Watch out for (4)

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 42 questions