Question : Directions: Select the correct combination of mathematical signs to sequentially replace the % signs and to balance the given equation.
[{(32 % 28) % (6 % 4)} % (1 % 7)] % 5 % 20
Option 1: −, +, ×, ÷, ×, ×, =
Option 2: ×, ÷, ×, ×, −, +, =
Option 3: ×, −, +, ×, ÷, ×, =
Option 4: −, +, ×, ×, ×, ×, =
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Correct Answer: −, +, ×, ÷, ×, ×, =
Solution :
Given:
[{(32 % 28) % (6 % 4)} % (1 % 7)] % 5 % 20
Replace % with the mathematical signs and solve the equations one by one using BODMAS.
Let's check the given options –
First option:
−, +, ×, ÷, ×, ×, =
⇒ [{(32 − 28) + (6 × 4)} ÷ (1 × 7)] × 5 = 20
Solving the L.H.S of the equation –
= {(4 + 24) ÷ 7} × 5
= (28 ÷ 7) × 5
= 20
Second option:
×, ÷, ×, ×, −, +, =
⇒ [{(32 × 28) ÷ (6 × 4)} × (1 − 7)] + 5 = 20
Solving the L.H.S of the equation –
= {(896 ÷ 24) × (−6)} + 5
= −224 + 5
= −219 ≠ 20
Third option:
×, −, +, ×, ÷, ×, =
⇒ [{(32 × 28) − (6 + 4)} × (1 ÷ 7)] × 5 = 20
Solving the L.H.S of the equation –
= {(896 − 10) × 0.14} × 5
= {886 × 0.14} × 5
= 124.04 × 5
= 620.2 ≠ 20
Fourth option:
−, +, ×, ×, ×, ×, =
⇒ [{(32 − 28) + (6 × 4)} × (1 × 7)] × 5 = 20
Solving the L.H.S of the equation –
= {(4 + 24) × (7)} × 5
= {28 × 7} × 5
= 196 × 5
= 980 ≠ 20
So, only the first option satisfies the given equation. Hence, the first option is correct.
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