Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
Option 1: 6 and 8
Option 2: 66 and 65
Option 3: 4 and 8
Option 4: 66 and 36
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Correct Answer: 4 and 8
Solution :
Given:
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
Interchange the numbers according to the given options –
First option:
6 and 8
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
⇒ [(√256) ÷ 4]³ + (8)² – (12 x 6) + 66 + (36 ÷ 12) = 65
⇒ [16 ÷ 4]³ + 64 – 36 + 66 + 3 = 65
⇒ [4]³ + 64 – 36 + 66 + 3 = 65
⇒ 64 + 64 – 36 + 66 + 3 = 65
⇒ 197 – 36 = 161 ≠ 65
Second option:
66 and 65
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
⇒ [(√256) ÷ 4]³ + (6)² – (12 x 8) + 65 + (36 ÷ 12) = 66
⇒ [16 ÷ 4]³ + 36 – 96 + 65 + 3 = 66
⇒ [4]³ + 36 – 96 + 65 + 3 = 66
⇒ 64 + 36 – 96 + 65 + 3 = 66
⇒ 168 – 96 = 72 ≠ 65
Third option:
4 and 8
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
⇒ [(√256) ÷ 8]³ + (6)² – (12 x 4) + 66 + (36 ÷ 12) = 65
⇒ [16 ÷ 8]³ + 36 – 48 + 66 + 3 = 65
⇒ [2]³ + 36 – 48 + 66 + 3 = 65
⇒ 8 + 36 – 48 + 66 + 3 = 65
⇒ 113 – 48 = 65
Fourth option:
66 and 36
[(√256) ÷ 4]³ + (6)² – (12 x 8) + 66 + (36 ÷ 12) = 65
⇒ [(√256) ÷ 4]³ + (6)² – (12 x 8) + 36 + (66 ÷ 12) = 65
⇒ [16 ÷ 4]³ + 36 – 96 + 36 + 5.5 = 65
⇒ [4]³ + 36 – 96 + 36 + 5.5 = 65
⇒ 64 + 36 – 96 + 36 + 5.5 = 65
⇒ 141.5 – 96 = 45.5 ≠ 65
So, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.
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