Question

a set of five positive integers has a mean median and range of 7 how many distant sets whose members are listed from least to greatest could have these properties

Answer 1

What properties?

Answer 2

a+b+c+d+e = 35 (mean=7)
c = 7 (median)
e = a+7 (range)

a+b+7+d+a+7 = 35
2a+b+d = 21

If a=1, b+d=19
But b<=7 and e=8
1,b,7,d,8
But, if b<=7, and d<=8, no go

If a=2, b+d=17
2,b,7,d,9
same problem as above

If a=3, b+d=15
d<=10, so b>=5
so we can have
3,b,7,d,10 as
<b>3,5,7,10,10
3,6,7,9,10
3,7,7,8,10</b>

If a=4, b+d=13
d <= 11, so b>=2. In fact, we know b>=4, so we can have
4,b,7,d,11
<b>4,4,7,9,11
4,5,7,8,11</b>

If a=5, b+d=11
d<=12,
5,b,7,d,12
no go, since b>=5, meaning d<=6, but d must be at least 7.

So, only the sets in boldface above are candidates.

Answer 3

You missed one! you could also count { 4, 6, 7, 7, 11}.