## If the average (arithmetic mean) of the five numbers $$x, 7, 2, 16$$ and $$11$$ is equal to the median of five numbers,

##### This topic has expert replies
Legendary Member
Posts: 2022
Joined: 14 Oct 2017
Followed by:3 members

### If the average (arithmetic mean) of the five numbers $$x, 7, 2, 16$$ and $$11$$ is equal to the median of five numbers,

by VJesus12 » Thu Mar 18, 2021 12:40 pm

00:00

A

B

C

D

E

## Global Stats

If the average (arithmetic mean) of the five numbers $$x, 7, 2, 16$$ and $$11$$ is equal to the median of five numbers, what is the value of $$x.$$

(1) $$7 < x < 11.$$
(2) $$x$$ is the median of the five numbers.

Source: GMAT Prep

Legendary Member
Posts: 2214
Joined: 02 Mar 2018
Followed by:4 members

### Re: If the average (arithmetic mean) of the five numbers $$x, 7, 2, 16$$ and $$11$$ is equal to the median of five numbe

by deloitte247 » Tue Mar 23, 2021 1:49 pm

00:00

A

B

C

D

E

## Global Stats

The numbers are x, 7, 2, 16, 11
$$\frac{x+7+2+16+11}{5}=median$$
Target question: what is the value of x?

Statement 1: 7 < x < 11
The possible values of x include 8, 9 and 10
Order of set => 2, 7, x, 11, 16. Irrespective of the value of x, it will still be the median.
$$Therefore,\ \frac{x+7+2+16+11}{5}=x$$
x + 36 = 5x
4x = 36
x = 36/4 = 9
Statement 1 is SUFFICIENT.

Statement 2: x is the median of the 5 numbers
$$\frac{2+7+x+11+16}{5}=x$$
This is the same as statement 1 above; hence, x = 9. Therefore, statement 2 is SUFFICIENT.

Since each statement is SUFFICIENT alone, the correct answer is option D

• Page 1 of 1