Question

Five whole numbers are written in order.

Answer 1

Answer:

• x = 7, y = 8

Step-by-step explanation:

Given numbers in order:

• 4, 6, x, y, 10

The mean is same as median.

The median is x as middle number. Since x is a whole number, the mean is also a whole number.

x and y can be selected from 7, 8 or 9 (numbers between 6 and 10).

The mean is:

• (4 + 6 + x + y + 10)/5 =
• (20 + x + y)/5 =
• 4 + (x + y)/5

It should be a whole number, so (x + y) should be divisible by 5.

The option is (7 + 8) = 15, and 9 is excluded.

Let's verify:

• Median = x = 7
• Mean = 4 + (7 + 8)/5 = 4 + 3 = 7

Answer 2

• 4,6,x,y,10

Mean:-

$\\ \sf\longmapsto \dfrac{4+6+x+y+10}{5}$

$\\ \sf\longmapsto \dfrac{x+y+20}{5}$

Median:-

• n=5
• M(D)=n+1/2=5+1/2=3rd term

$\\ \sf\longmapsto M(D)=x$

Compare

$\\ \sf\longmapsto \dfrac{x+y+20}{5}=x$

$\\ \sf\longmapsto x+y+20=5x$

$\\ \sf\longmapsto 4x=y+20$

$\\ \sf\longmapsto x=y/4+5$

$\\ \sf\longmapsto x$

Take pair of (7,8)

$\\ \sf\longmapsto 7=8/4+5\implies 7=2+5$

Verified

Hence

• x=7
• y=8