Which two signs should be interchanged to make the following equation correct? 139 + 40 ÷ 5 − 168 × 3 = 283

Correct — C. Interchange ÷ and ×, then read the new line under BODMAS.

The line becomes 139 + 40 × 5 − 168 ÷ 3.

40 × 5 = 200
168 ÷ 3 = 56
139 + 200 = 339
339 − 56 = 283

That is the required right-hand side, so option (c) is the swap that balances the equation.

Why the others are wrong

• (a)
  + and ÷ — The line becomes 139 ÷ 40 + 5 − 168 × 3. The 504 produced by 168 × 3 drags the total to about −495, nowhere near 283.
• (b)
  − and × — The line becomes 139 + 40 ÷ 5 × 168 − 3. The chain 8 × 168 pushes the total to 1,480, more than five times the target.
• (d)
  − and + — The line becomes 139 − 40 ÷ 5 + 168 × 3 = 635, because 168 × 3 now arrives with a plus sign instead of a minus.

A sign-interchange item is a BODMAS drill in disguise. Nothing is being solved for; four rewrites are being tested and the one that balances is kept.

Because × and ÷ are settled before + and −, moving a sign onto a large term changes the total far more than moving it onto a small one. Here 168 is the biggest number on the line, so its fate decides the answer: divided by 3 it contributes 56, multiplied by 3 it contributes 504.

Key facts

• Under BODMAS, × and ÷ are settled before + and −, working left to right.
• With ÷ and × interchanged the line reads 139 + 40 × 5 − 168 ÷ 3 = 283.
• Testing what each swap does to the largest term, 168, eliminates two options in one step.

Common traps

• Applying the swap to one occurrence of a sign and leaving the other in place
• Working left to right and adding 139 + 40 before the multiplication
• Testing options in the printed order instead of starting from the biggest term

No directly related past PYQ was found.