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There are 4 consecutive odd numbers, x1 , x2 , x3 and x4 and three consecutive even numbers y1 , y2 and y3 . The average of the odd numbers is 6 less than the average of the even numbers. If the sum of the three even numbers is 16 less than the sum of the four odd numbers, what is the average of x1 , x2, x3 and x4?

There are 4 consecutive odd numbers, x1 , x2 , x3 and x4 and three consecutive even numbers y1 , y2 and y3 . The average of the odd numbers is 6 less than the average of the even numbers. If the sum of the three even numbers is 16 less than the sum of the four odd numbers, what is the average of x1 , x2, x3 and x4? Correct Answer 34

Calculation:

Average of four given consecutive odd nubmers =  (x1 +  x2 + x3 + x4)/4

Average of three given consecutive even numbers = (y1 + y2 + y3)/3

ATQ, ( x1 +  x2 + x3 + x4)/4  = (y1 + y2 + y3)/3 — 6      ----(1)

(y1 + y2 + y3) =  ( x1 +  x2 + x3 + x4) — 16      ----(2)

Substituting (2) in (1),

(x1 +  x2 + x3 + x4)/4 = /3 — 6     

⇒ (x1 + x2 + x3 + x4) × (1/4 — 1/3) = (-16 — 18)/3  

⇒ (x1 +  x2 + x3 + x4)/4 = 34/3 × 3 = 34

∴ Average of odd numbers is 34.

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