Question : Directions: Which two numbers from the given options should be interchanged to make the given equation correct?
54 – (3 × 12) ÷ (8)1/3 + (11 × 4) + 6 = 69
Option 1: 11 and 6
Option 2: 4 and 12
Option 3: 6 and 4
Option 4: 3 and 4
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Correct Answer: 3 and 4
Solution :
Given:
54 – (3 × 12) ÷ (8)
1/3
+ (11 × 4) + 6 = 69
Let's check the options –
First option:
11 and 6
On interchanging the numbers, we get –
⇒ 54 – (3 × 12) ÷ (8)
1/3
+ (6 × 4) + 11 = 69
Solving the L.H.S. of the equation –
= 54 – (3 × 12) ÷ (8)
1/3
+ (6 × 4) + 11
= 54 – 36 ÷ 2 + 24 + 11
= 54 – 18 + 24 + 11
= 89 – 18
= 71 ≠ 69
Second option:
4 and 12
On interchanging the numbers, we get –
⇒ 54 – (3 × 4) ÷ (8)
1/3
+ (11 × 12) + 6 = 69
Solving the L.H.S. of the equation –
= 54 – (3 × 4) ÷ (8)
1/3
+ (11 × 12) + 6
= 54 – 12 ÷ 2 + 132 + 6
= 54 – 6 + 132 + 6
= 192 – 6
= 186 ≠ 69
Third option:
6 and 4
On interchanging the numbers, we get –
⇒ 54 – (3 × 12) ÷ (8)
1/3
+ (11 × 6) + 4 = 69
Solving the L.H.S. of the equation –
= 54 – (3 × 12) ÷ (8)
1/3
+ (11 × 6) + 4
= 54 – 36 ÷ 2 + 66 + 4
= 54 – 18 + 66 + 4
= 124 – 18
= 106 ≠ 69
Fourth option:
3 and 4
On interchanging the numbers, we get –
⇒ 54 – (4 × 12) ÷ (8)
1/3
+ (11 × 3) + 6 = 69
Solving the L.H.S. of the equation –
= 54 – (4 × 12) ÷ (8)
1/3
+ (11 × 3) + 6
= 54 – 48 ÷ 2 + 33 + 6
= 54 – 24 + 33 + 6
= 93 – 24
= 69
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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