Question : Directions: Select the correct combination of mathematical signs to sequentially replace the & signs, and to balance the given equation. [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10
Option 1: ×, ÷, ×, ×, −, +, =
Option 2: ×, −, +, ×, ÷, ×, =
Option 3: −, +, ×, ×, ÷, ×, =
Option 4: −, +, ×, ÷, ×, ×, =
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Correct Answer: −, +, ×, ÷, ×, ×, =
Solution : Given: [{(42 & 26) & (12 & 2)} & (4 & 5)] & 5 & 10
Replace & with the mathematical signs and solve the equations one by one using BODMAS. First option: ×, ÷, ×, ×, −, +, = ⇒ [{(42 × 26) ÷ (12 × 2)} × (4 – 5)] + 5 = 10 Solving the L.H.S. of the equation – = [{(1092) ÷ (24)} × (–1)] + 5 = [{45.5} × (–1)] + 5 = –45.5 + 5 = –40.5 ≠ 10 Second option: ×, −, +, ×, ÷, ×, = ⇒ [{(42 × 26) – (12 + 2)} × (4 ÷ 5)] × 5 = 10 Solving the L.H.S. of the equation – = [{(1092) – (14)} × (0.8)] × 5 = [{1078} × (0.8)] × 5 = 862.4 × 5 = 4312 ≠ 10 Third option: −, +, ×, ×, ÷, ×, = ⇒ [{(42 – 26) + (12 × 2)} × (4 ÷ 5)] × 5 = 10 Solving the L.H.S. of the equation – = [{16 + 24} × (0.8)] × 5 = [40 × 0.8] × 5 = 32 × 5 = 160 ≠ 10 Fourth option: −, +, ×, ÷, ×, ×, = ⇒ [{(42 – 26) + (12 × 2)} ÷ (4 × 5)] × 5 = 10 Solving the L.H.S. of the equation – = [{16 + 24} ÷ (20)] × 5 = [40 ÷ 20] × 5 = 2 × 5 = 10
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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