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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