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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