What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged? 4 + 9 × 48 – 6 ÷ 7 = ?
- (a)41
- (b)37
- (c)27
- (d)30
Answer
Why
Correct — B.
Rule: rewrite the line with the swapped symbols, then apply BODMAS.
This stem pairs ÷ with − and × with +. So 4 + 9 × 48 − 6 ÷ 7 becomes
4 × 9 + 48 ÷ 6 − 7
Divide: 48 ÷ 6 = 8
Multiply: 4 × 9 = 36
Then 36 + 8 − 7 = 37
That is option (b).
Why the others are wrong
- (a)41 — The first two terms of the swapped line already give 44, and 7 comes off, not 3. 41 would need a 3 that the equation does not contain.
- (c)27 — 27 would need the 4 × 9 to come to 26, since 26 + 8 − 7 = 27. The swap changes symbols only, and 4 × 9 = 36 stands.
- (d)30 — 30 needs the middle term to be 1 rather than 8, because 36 + 1 − 7 = 30. But ÷ replaces −, so 48 ÷ 6 = 8 is what enters the sum.
Concept
Interchange items are two exercises stacked: a substitution, then an order-of-operations calculation.
Read the pairing off this stem rather than from memory. Here it is ÷ with − and × with +, so every ÷ printed becomes a −, every − becomes a ÷, every × becomes a +, and every + becomes a ×.
Once the new line is on paper, ordinary BODMAS finishes it: division and multiplication first, then addition and subtraction from left to right.
The swap is not symmetric in effect. It moves the heavy operation — a division — into the middle of the line and pushes the multiplication to the front, so a candidate working left to right on the printed line gets nowhere near 37.
Key facts
- The pairs named in this stem are ÷ with − and × with +.
- After the swap the line reads 4 × 9 + 48 ÷ 6 − 7.
- BODMAS on that line gives 36 + 8 − 7 = 37.
Study next
Common traps
- Carrying a pairing over from another question instead of reading the one this stem names
- Evaluating the printed line and then swapping the result
The same in-the-place-of-? wording is also used at 9 Sep 2024, 09:00, Reasoning Q.8 (5 − 4 ÷ 9 + 80 × 10) and 9 Sep 2024, 12:30, Reasoning Q.25.
Related PYQs
No directly related past PYQ was found.