Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct? 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) – 11 = 112
Option 1: 18 and 11
Option 2: 12 and 4
Option 3: 6 and 4
Option 4: 18 and 12
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Correct Answer: 6 and 4
Solution : Given: 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 Interchange the numbers given in the options one by one with the original numbers in the given equation.
First option: 18 and 11 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 ⇒ 11 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 18 = 112 = 11 + 72 + 9 x 4 + 3 – 18 = 112 = 11 + 72 + 36 + 3 – 18 = 112 = 122 – 18 = 104 ≠ 112 Second option: 12 and 4 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 ⇒ 18 + (4 x 6) + (63 ÷ 7) x 12 + (27) ⅓ – 11 = 112 =18 + 24 + 9 x 12 + 3 – 11 = 112 =18 + 24 + 108 + 3 – 11 = 112 =153 – 11 = 142 ≠ 112 Third option: 6 and 4 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 ⇒ 18 + (12 x 4) + (63 ÷ 7) x 6 + (27) ⅓ – 11 = 112 =18 + 48 + 9 x 6 + 3 – 11 = 112 =18 + 48 + 54 + 3 – 11 = 112 =123 – 11 = 112 = R.H.S Fourth option: 18 and 12 18 + (12 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 ⇒ 12 + (18 x 6) + (63 ÷ 7) x 4 + (27) ⅓ – 11 = 112 = 12 + 108 + 9 x 4 + 3 – 11 = 112 = 12 + 108 + 36 + 3 – 11 = 112 = 159 – 11 = 148 ≠ 112
So, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.
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