There are 4 consecutive odd numbers (x1 x2 x3 and x4)…

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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?

  1. A. 30
  2. B. 38
  3. C. 32
  4. D. 34

Answer: Option D

Here is complete explanation of There are 4 consecutive odd numbers (x1 x2 x3 and x4)….

Solution(By ExamCraze Team)

According to given information
Average of odd numbers = Average of even numbers - 6
$$ Rightarrow frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} = $$     $$frac{{{y_1} + {y_2} + {y_3}}}{3} - 6$$
$$ Rightarrow frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} = $$     $$frac{{{y_1} + {y_2} + {y_3} - 18}}{3}$$
$$ Rightarrow 3left( {{x_1} + {x_2} + {x_3} + {x_4}} right) = $$     $$4left( {{y_1} + {y_2} + {y_3}} right) - 72$$
Also,
$$ Rightarrow {y_1} + {y_2} + {y_3} = $$     $${x_1} + {x_2} + {x_3} + {x_4} - 16$$
$$ Rightarrow {x_1} + {x_2} + {x_3} + {x_4} = $$     $${y_1} + {y_2} + {y_3} + 16$$   .....(i)
So we have,
$$ Rightarrow 3left( {{y_1} + {y_2} + {y_3} + 16} right) = $$     $$4left( {{y_1} + {y_2} + {y_3}} right) - 72$$
$$ Rightarrow 3{y_1} + 3{y_2} + 3{y_3} + 48 = $$     $$4{y_1} + 4{y_2} + 4{y_3} - 72$$
$$ Rightarrow 4{y_1} + 4{y_2} + 4{y_3}$$   $$ - 3{y_1} - 3{y_2} - 3{y_3}$$     = 48 + 72
$$ Rightarrow {y_1} + {y_2} + {y_3} = 120$$
$$ Rightarrow {x_1} + {x_2} + {x_3} + {x_4}$$     = 120 + 16 = 136 [From (i)]
∴ Average of four odd numbers :
$$eqalign{ & = frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} cr & = frac{{136}}{4} cr & = 34 cr} $$

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