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?

A. 30

B. 38

C. 32

D. 34

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Solution(By Apex Team)

According to given information Average of odd numbers = Average of even numbers – 6 $\begin{array}{l}\Rightarrow\Large\frac{x_1+x_2+x_3+x_4}{4}=\frac{y_1+y_2+y_3}{3}-6\\ \Rightarrow\Large\frac{x_1+x_2+x_3+x_4}{4}=\frac{y_1+y_2+y_3-18}{3}\\ \Rightarrow3\left(x_1+x_2+x_3+x_4\right)=4\left(y_1+y_2+y_3\right)-72\\ \text{ Also, }\\ \Rightarrow y_1+y_2+y_3=x_1+x_2+x_3+x_4-16\\ \Rightarrow x_1+x_2+x_3+x_4=y_1+y_2+y_3+16\ldots\ldots\text{ (i) }\\ \text{So, we have,}\\ \Rightarrow3\left(y_1+y_2+y_3+16\right)=4\left(y_1+y_2+y_3\right)-72\\ \Rightarrow3y_1+3y_2+3y_3+48=4y_1+4y_2+4y_3-72\\ \Rightarrow4y_1+4y_2+4y_3-3y_1-3y_2-3y_3=48+72\\ \Rightarrow y_1+y_2+y_3=120\\ \Rightarrow x_1+x_2+x_3+x_4=120+16=136\text{ [From (i)] }\\ \therefore\text{ Average of four odd numbers : }\\ =\Large\frac{x_1+x_2+x_3+x_4}{4}\\ =\Large\frac{136}{4}\\ =34\end{array}$

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