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If the average of five consecutive even numbers is 38, what is the difference between the square of the largest and the smallest?
- A484
- B576
- C608
- D712
Answer not set
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CCommunity
Let the five consecutive even numbers be X, X + 2, X + 4, X + 6, X + 8
Given the average of these numbers = 38
⇒ Combined Sum of the all the five consecutive even numbers = (Average) × (Total no. of numbers)
⇒ X + (X + 2) + (X + 4) + (X + 6) + (X + 8) = (38 × 5)
⇒ 5X + 20 = 190
⇒ 5X = 190 – 20 = 170
⇒ X = 170/5 = 34
So the Largest number = 34 + 8 = 42 and Smallest number = 34
∴ Difference between their squares = 422 – 342 = 1764 – 1156 = 608
Given the average of these numbers = 38
⇒ Combined Sum of the all the five consecutive even numbers = (Average) × (Total no. of numbers)
⇒ X + (X + 2) + (X + 4) + (X + 6) + (X + 8) = (38 × 5)
⇒ 5X + 20 = 190
⇒ 5X = 190 – 20 = 170
⇒ X = 170/5 = 34
So the Largest number = 34 + 8 = 42 and Smallest number = 34
∴ Difference between their squares = 422 – 342 = 1764 – 1156 = 608