SSC CGL Reasoning · Mathematical Operations

Value After Interchanging Signs

When 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.

All Mathematical Operations notes

Why this matters

Fifty-seven questions in the bank, all EASY, and 56 of them come from the 2024 shifts, where this was the most common Mathematical Operations question. In 45 of them the swaps are + with − and × with ÷; the other 12 move a sign to a different level, which changes what is worked out first.

Concept 1 of 2: Plus with minus, times with divide

Swapping + with − and × with ÷ keeps the shape of the row. Wherever there was a product or a quotient there is still one, only turned round, so you work the row block by block as before.

Definition

‘+ and − are interchanged’ means every + becomes − and every − becomes +.
Copy the row once with both swaps made, reading each sign from the printed row.
Inside a block, keep the left-to-right order: $a \times b \div c$ becomes $a \div b \times c$ , worked from the left.
Work out each block, then the additions and subtractions from left to right.
Fast route: the blocks sit in the same places before and after the swap, so mark them on the printed row first. Then only the numbers inside each block, and the + or − in front of it, need rewriting.

Worked example

What will come in place of ? if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged:

63 - 72 \times 8 \div 3 + 11 = ?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 22 Sep 2025, Shift 1 · Q20Easy

Example 1 · Mathematical Operations · Value After Interchanging Signs

Given below is an equation which has to be solved by following the interchange i.e., + becomes

-

and

-

becomes +

\times

becomes

\div

and

\div

becomes

\times

Then what is the value of 100

\div

5 + 20

-

\times

2 = ?

Swapping in one direction only

Interchanged means both ways. If every + becomes − but the − signs are left alone, two terms change instead of all of them and the total is wrong.

Changing the order inside a block

a \times b \div c

becomes

a \div b \times c

, worked from the left. Dividing

a

by the product

b \times c

gives a different number.

Drill 44 more on plus with minus, times with divide

Concept 2 of 2: Swaps across the levels

When + is swapped with × (or − with ÷, or + with ÷), the blocks move. A sum turns into a product and a product into a sum, so the row has a new shape. Rewrite it in full before you work anything out.

Definition

Rewrite every sign from the printed row, using both pairs.
Then find the new blocks of × and ÷ and work them first; the old products mean nothing now.
A one-way list (‘×’ is replaced by ‘÷’, ‘÷’ by ‘+’, ‘+’ by ‘×’) is not a pair of swaps: follow each arrow once. A sign the list leaves alone stays as it is.
A fraction inside a block is not a mistake: $27 \div 6 \times 4 = 4.5 \times 4 = 18$ . Only the final value has to match an option.

Worked example

What will come in place of ? if ‘+’ and ‘÷’ are interchanged and ‘−’ and ‘×’ are interchanged:

56 + 7 - 3 \div 9 \times 4 = ?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 13 Sep 2024, Shift 3 · Q17Easy

Example 2 · Mathematical Operations · Value After Interchanging Signs

What will come in place of the question mark (?) in the following equation if '+' and '

\times

' are interchanged and '

-

' and '

\div

' are interchanged?

27 - 6 + 4 \times 8 \div 6 = ?

Keeping the old products

After + and × are interchanged,

6 + 5 \times 4

6 \times 5 + 4 = 34

. Working out the printed

5 \times 4

first and then swapping the signs gives a wrong total.

Treating a one-way list as swaps

If × is replaced by ÷ and ÷ by +, a ÷ in the row becomes +, not ×. Only the word interchanged means a two-way swap.

Drill 11 more on swaps across the levels

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.

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

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 test Drill all 57 questions