I have a math logic question, Please help!?

Question

In a group of five friends, the sums of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest?

Please show work or thought process.

Thanks!

Answer 1

a + b + c + d = 124
a + b + c + e = 128
a + b + d + e = 130
a + c + d + e = 136
b + c + d + e = 142

Add these all up and you get 4a + 4b + 4c + 4d + 4e = 660
a + b + c + d + e = 660/4 = 165

The largest sum is 142, which means that's the one that leaves out the youngest. The youngest is therefore 165-142 = 23 years old.

Answer 2

The youngest (in fact any one of the five) must be in all but one group. So the youngest cannot be in the group of 142, likewise the oldest person cannot be in the group of 124. Also note that as each group of four has different values no person can have the same age. So I will denote the ages from youngest to oldest as a,b,c,d,e. This means that e is not in 124, d not in 128, c not in 130, b not in 136 and a not in 142 (if it's not clear why I will post again). We will get b,c,d,e in terms of a and then solve for a. I will find b explicitly then just tell you my results for the others and you can verify by following the method for finding b. (e+d+c+b) - (e+d+c+a) = b-a = 142 - 136= 6 so that b=6+a.

(e+d+c+b) - (e+d+b+a)= c-a= 12 so c=12+a
(e+d+c+b) - (e+c+b+a) =d-a= 14 so d =14+a
(e+d+c+b) - (d+c+b+a)= e -a=18 so e=18+a

Now 142 = 4a + 50 so that 4a = 92 and after dividing we get that a = 23.

Answer 3

Let the sum of the ages of all 5 friends be M

Then the sum of the ages of each group of 4 differs from M by the age of the omitted friend.

The omitted friend from group 1 is M-124
The omitted friend from group 2 is M-128
The omitted friend from group 3 is M-130
The omitted friend from group 4 is M-136
The omitted friend from group 5 is M-142

So the sum of the ages of the omitted friends is

5M-(124+128+130+136+142)

But this is just the sum of all 5 friends which is M so they should be equal.

5M-(124+128+130+136+142) = M

4M = 124+128+130+136+142

4M = 660

M = 165

The youngest person is the person who is omitted from the "oldest" group, which is group 5

omitted friend 5 is 165 - 142 = 23

Answer 4

If we add up all of these numbers, then we'll be counting each person's age exactly four times. So the sum will be 4 times the sum of all five ages.

The highest of the original sums must be the sum of the four highest ages. So subtract this from the result we got above, and you'll have the youngest age.

Answer 5

the youngest is 23 years old

Answer 6

a+b+c+d+e=124
b+c+d+e+f=128
c+d+e+f+a=130
d+e+f+a+b=136
e+f+a+b+c=142
adding all above equations
4(a+b+c+d+e+f)=660
a+b+c+d+e+f=165
there fore
age of youngest is
165-142=23years

Answer 7

let the friends 'names be A,B,C,D,Eand let their ages bea,b,c,d &e
groups
1)A,B,C,D: a=b=c=d=124
2)A,B,D,E; a+b+d+e=128
3)A,BC,Ea+b+c+e=130.
4)A,C,D,E: a+c+d+e=136.
5)B,C,D,E+b+c+d+e=142