Which two numbers (not digits) should be interchanged to make the given equation correct? 116 - 92 ÷ 4 + 25 × 2 - 20 = 150

Correct — A. Work the printed equation first, under BODMAS, so you know how big a change the swap must make.

116 − 92 ÷ 4 + 25 × 2 − 20
= 116 − 23 + 50 − 20
= 123, which is 27 short of 150.

Rule: interchange 2 and 4, then re-apply BODMAS.

116 − 92 ÷ 2 + 25 × 4 − 20
= 116 − 46 + 100 − 20
= 70 + 100 − 20
= 150 → option (a)

The division loses 23 and the multiplication gains 50, a net change of exactly +27.

Why the others are wrong

• (b)
  25 and 20 — 116 − 92 ÷ 4 + 20 × 2 − 25 = 116 − 23 + 40 − 25 = 108. Swapping the two end terms leaves 92 ÷ 4 untouched, and the division is where the shortfall sits.
• (c)
  116 and 92 — 92 − 116 ÷ 4 + 25 × 2 − 20 = 92 − 29 + 50 − 20 = 93. Moving 116 into the division makes the total smaller, not larger.
• (d)
  20 and 92 — 116 − 20 ÷ 4 + 25 × 2 − 92 = 116 − 5 + 50 − 92 = 69, the furthest of the four from 150.

Interchange questions ask you to test, not to solve. There is no algebra to do — four swaps are offered and one of them balances the equation.

Compute the printed value first. It tells you the size and the sign of the change you need, and it often kills two options before you evaluate them.

Then remember which operations the swap touches. A number sitting inside a division or a multiplication has far more leverage than one being added or subtracted at the end.

Key facts

• BODMAS: brackets and orders first, then division and multiplication, then addition and subtraction.
• As printed the expression equals 123, so the swap has to add 27.
• Swapping 2 and 4 turns 92 ÷ 4 = 23 into 92 ÷ 2 = 46 and 25 × 2 = 50 into 25 × 4 = 100.

Common traps

• Working left to right instead of applying BODMAS.
• Swapping digits when the stem says numbers.
• Testing options in the printed order without first evaluating the equation as given.

No directly related past PYQ was found.