Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
78 + 456 − 45 × 12 ÷ 4 = 519
Option 1: 12 and 4; − and ×
Option 2: 78 and 456; ÷ and ×
Option 3: 45 and 12; + and ÷
Option 4: 456 and 45; ÷ and −
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Correct Answer: 78 and 456; ÷ and ×
Solution :
Given:
78 + 456 − 45 × 12 ÷ 4 = 519
Interchange the numbers and signs in the options one by one in the given equation.
First option:
12 and 4; − and ×
78 + 456 − 45 × 12 ÷ 4 = 519
⇒ 78 + 456 × 45 – 4 ÷ 12 = 519
⇒ 78 + 456 × 45 − 0.33
⇒ 78 + 20520 − 0.33
⇒ 20597.67 ≠ 519
Second option:
78 and 456; ÷ and ×
78 + 456 − 45 × 12 ÷ 4 = 519
⇒ 456 + 78 − 45 ÷ 12 × 4 = 519
⇒ 456 + 78 − 3.75 × 4
⇒ 456 + 78 − 15
⇒ 519 = 519 = R.H.S.
Third option:
45 and 12; + and ÷
78 + 456 − 45 × 12 ÷ 4 = 519
⇒ 78 ÷ 456 − 12 × 45 + 4 = 519
⇒ 0.17 − 12 × 45 + 4
⇒ 0.17 − 540 + 4
⇒ 4.17 − 540
⇒ - 535.83 ≠ 519
Fourth option:
456 and 45; ÷ and −
78 + 456 − 45 × 12 ÷ 4 = 519
⇒ 78 + 45 ÷ 456 × 12 − 4 = 519
⇒ 78 + 0.1 × 12 − 4
⇒ 78 + 1.2 − 4
⇒ 79.2 − 4
⇒ 75.2 ≠ 519
So, only the second option satisfies the R.H.S. of the given equation. Hence, the second option is correct.
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