Question

PLEASE HELP, URGENT, POINTS GIVEN

A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.

Answer 1

19, 29, 29, 37, 41

Explanation:

1. What we know: x y 29 z 41

(x+y+29+z+41)/5 =31

x y and z each >9 and prime

Possibile numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41

2. (x+y+29+z+41)/5 =31

x+y+29+z+41 = (31×5)

x+y+z = (31×5) -29 -41

x+y+z = 85

z>=29

x<=29

y<=29

x and y can be 11, 13, 17, 19, 23, 29

z could be 29, 31, 37, 41

At least one if them must equal 29 because it's the mode.

So two of them must equal 56

11+29=40 so both numbers cannot be less than or equal to 40

This means y is 29 because x + z has to equal 56 and that wouldn't be possible if x equals 29.

Now we know x+z=56

Possible numbers: 19+37

I found these by doing 56- each possible number for x and seeing if that equaled a possible number for z. For example 56-11=45 but z cannot be 45 therefore x cannot be 11 and so on.

Then you just plug in the numbers!

19, 29, 29, 37, 41

This was so much fun to solve! I hope this is helpful, let me know if you have any questions! You got this :)