If x

Question

If x<y<2 x; the median and the mean of x, y, and 2 x are 27 and 33 , respectively, then find the mean of x and &gamma;. (A) 23.5 (B) 24 (C) 23 (D) 25.5

Tardigrade Admin · Accepted Answer

As x, y and 2 x are in ascending order, median is &gamma;. y=27 text Mean =(x+y+2 x/3)=33 ⇒ (3 x+27/3)=33 ⇒ x=24 . ∴ Mean of x and &gamma;=(x+y/2) ⇒ (24+27/2)=25.5.

Q. If $x < y < 2 x$ ; the median and the mean of $x, y$ , and $2 x$ are 27 and 33 , respectively, then find the mean of $x$ and $γ$ .

23.5

24

23

25.5

As $x, y$ and $2 x$ are in ascending order, median is $γ$ . $y = 27$
$Mean = \frac{x + y + 2 x}{3} = 33$
$\Rightarrow \frac{3 x + 27}{3} = 33 \Rightarrow x = 24.$
$∴$ Mean of $x$ and $γ = \frac{x + y}{2} \Rightarrow \frac{24 + 27}{2} = 25.5$ .

Q. If x<y<2x; the median and the mean of x,y, and 2x are 27 and 33 , respectively, then find the mean of x and γ.

23.5

24

23

25.5

As x,y and 2x are in ascending order, median is γ. y=27 Mean =3x+y+2x​=33 ⇒33x+27​=33⇒x=24. ∴ Mean of x and γ=2x+y​⇒224+27​=25.5.

Q. If $x < y < 2 x$ ; the median and the mean of $x, y$ , and $2 x$ are 27 and 33 , respectively, then find the mean of $x$ and $γ$ .

As $x, y$ and $2 x$ are in ascending order, median is $γ$ . $y = 27$
$Mean = \frac{x + y + 2 x}{3} = 33$
$\Rightarrow \frac{3 x + 27}{3} = 33 \Rightarrow x = 24.$
$∴$ Mean of $x$ and $γ = \frac{x + y}{2} \Rightarrow \frac{24 + 27}{2} = 25.5$ .