Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?
(6)³ ÷ 12 + [(√81) x 4] – (28 ÷ 2) + 24 = 43
Option 1: 12 and 24
Option 2: 6 and 24
Option 3: 81 and 4
Option 4: 28 and 24
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Correct Answer: 12 and 24
Solution :
Given:
(6)³ ÷ 12 + [(√81) x 4] – (28 ÷ 2) + 24 = 43
Interchanging the numbers as given in the options –
First option:
12 and 24
(6)³ ÷ 24 + [(√81) x 4] – (28 ÷ 2) + 12 = 43
⇒ 216 ÷ 24 + (9 x 4) – 14 + 12 = 43
⇒ 216 ÷ 24 + 36 – 14 + 12 = 43
⇒ 9 + 36 – 14 + 12 = 43
⇒ 57 – 14 = 43 = R.H.S
Second option:
6 and 24
(24)³ ÷ 12 + [(√81) x 4] – (28 ÷ 2) + 6 = 43
⇒ 13824 ÷ 12 + (9 x 4) – 14 + 6 = 43
⇒ 13824 ÷ 12 + 36 – 14 + 6 = 43
⇒ 1152 + 36 – 14 + 6 = 43
⇒ 1152 + 36 – 14 + 6 = 43
⇒ 1194 – 14 = 1180 ≠ 43
Third option:
81 and 4
(6)³ ÷ 12 + [(√4) x 81] – (28 ÷ 2) + 24 = 43
⇒ 216 ÷ 12 + (2 x 81) – 14 + 24 = 43
⇒ 216 ÷ 12 + 162 – 14 + 24 = 43
⇒ 18 + 162 – 14 + 24 = 43
⇒ 204 – 14 = 43 = 190 ≠ 43
Fourth option:
28 and 24
(6)³ ÷ 12 + [(√81) x 4] – (24 ÷ 2) + 28 = 43
⇒ 216 ÷ 12 + (9 x 4) – 12 + 28 = 43
⇒ 216 ÷ 12 + 36 – 12 + 28 = 43
⇒ 18 + 36 – 12 + 28 = 43
⇒ 82 – 12 = 70 ≠ 43
So, only the first option satisfies the R.H.S. of the given equation. Hence, the first option is correct.
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