Which number will come in the place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 7 ÷ 5 − 30 × 6 + 4 = ?

Correct — B. Rewrite the line with the symbols exchanged, then work it by BODMAS.

Given: 7 ÷ 5 − 30 x 6 + 4
After + and − are swapped and x and ÷ are swapped: 7 x 5 + 30 ÷ 6 − 4

7 x 5 = 35
30 ÷ 6 = 5
35 + 5 = 40
40 − 4 = 36 → option (b)

Why the others are wrong

• (a)
  32 — 32 is 36 with the 4 taken off twice. The swapped line carries one minus sign and one 4, so that subtraction happens once.
• (c)
  30 — 30 is 35 − 5, the two products differenced. It keeps the printed minus sign instead of swapping it, and never uses the final 4.
• (d)
  34 — 34 = 35 − 5 + 4. Here x and ÷ were swapped but + and − were left as printed. Both pairs are interchanged, which turns that middle sign into a plus.

Two instructions are stacked in this item, and each has its own failure mode.

First, rewrite the line with the symbols exchanged — every + becomes −, every − becomes +, every x becomes ÷, every ÷ becomes x. Write it out; doing it in your head is where the mark goes.

Second, work the new line by BODMAS, not left to right. Multiplication and division are settled before addition and subtraction, so 7 x 5 + 30 ÷ 6 − 4 is 35 + 5 − 4.

Key facts

• After the swap the expression reads 7 x 5 + 30 ÷ 6 − 4.
• BODMAS settles x and ÷ before + and −, so 35 and 5 are formed first.
• 35 + 5 − 4 = 36.
• Leaving + and − unswapped gives 35 − 5 + 4 = 34, which is one of the printed options.

Common traps

• Swapping x and ÷ but leaving + and − as printed, which lands on 34
• Working the swapped line strictly left to right instead of by BODMAS

No directly related past PYQ was found.