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The mean of the three numbers is 38 and the range of data is 31. The middle number is 20 less than the sum of the other two numbers. What is the largest number among these three numbers?1. 472. 493. 514. 45 |
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Answer» Correct Answer - Option 2 : 49 Given: Mean = 38 Range = 31 The middle number is 20 less than the sum of the other two numbers Formula used: Mean = (x + y + z)/3 Range = biggest term – smallest term Calculation: Let the three numbers is x, y, and z. Mean = (x + y + z)/3
⇒ 38 = (x + y + z)/3 ⇒ x + y + z = 114 ….(i) According to question, Middle term = (first term + last term) – 20 ⇒ y = (x + z) – 20 Value of y putting in equation (i) ⇒ x + z + (x + z) – 20 = 114 ⇒ 2(x + z) =134 ⇒ x + z = 67 ….(ii) According to question Rang = biggest term – smallest term ⇒ z – x = 31 ….(iii) add the equation of (ii) and (iii) ⇒ 2z = 98 ⇒ z = 49 ∴ The largest number is 49. |
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