Which two signs should be interchanged to make the following equation CORRECT? [{(15 + 3) − (4 × 2)} ÷ (4 − 6)] × 5 = 10

Correct — A.
Rule: swap every occurrence of both signs, then solve the inner brackets first.

Swap + and −: [{(15 − 3) + (4 × 2)} ÷ (4 + 6)] × 5
Brackets: 12 + 8 = 20, and 4 + 6 = 10
20 ÷ 10 = 2, then 2 × 5 = 10 → option (a).

Why the others are wrong

• (b)
  + and × — + and × also turns the final × 5 into + 5: (45 − 6) ÷ (4 − 6) + 5 = 39 ÷ (−2) + 5 = −14.5, not 10.
• (c)
  + and ÷ — + and ÷ gives {(15 ÷ 3) − 8} + (4 − 6), that is −3 + (−2) = −5, and × 5 makes −25, not 10.
• (d)
  × and ÷ — × and ÷ turns the divisor into a multiplier: (18 − 2) × (4 − 6) = −32, and the final ÷ 5 gives −6.4, not 10.

A sign-interchange item names two signs and swaps every place each one appears. Rewrite the whole equation for each option before you evaluate it.

Here − appears twice and × appears twice. Swapping + and − changes three signs, including the − inside (4 − 6). That change turns the divisor from −2 into 10, which is what brings the total to 10.

Key facts

• Interchanging two signs changes every occurrence of both, not just the first.
• Brackets are solved innermost first: ( ), then { }, then [ ].
• As printed the left side equals −25, and after swapping + and − it equals 10.

Common traps

• Swapping only the first − and leaving (4 − 6) alone, which gives 20 ÷ (−2) × 5 = −50
• Forgetting that the × before 5 also changes when × is one of the swapped pair

No directly related past PYQ was found.