a family has only one son. The father says "After x

Question

a family has only one son. The father says "After 'x' years, my age will be six times the age of my son". The mother says, "After X years, my age will be 4 times the age of my son". What will be the combined age (integer value) of the thee-member family after 'x' years ?

1. the age difference between the parents is 16 years.
2. After 'x' years the son will be twice as old as he is now

1. the age difference between the parents is 16 years.
2. After 'x' years the son will be twice as old as he is now

chetan2u · Answer

Hi..
Let the kids age be y..
So father's age = 6y and mother's age = 4y..
Combined age = 11y..
So we require value of y..

Statement I
Age difference in parents is 16...
So 6y-4y=16...2y=16...y=8
Sufficient

Statement II
After x years the son will be twice as of now..
We are still playing with variable..
Only new info y=x..
Insufficient

A

blueviper · Answer

F, M, S=Father's, Mother's & Son's initial age. F + x = 6(S + x) .... (I) M + x = 4(S + x) .... (II) We need to find the value of F + M + S + 3x 1) |F-M| = 16 Now, if we subtract the equations, (I) - (II), we get F - M = 2(S + x) or S + x = 8 .... (III) Now, if we add the equations, (I) + (II), we get F + M + 2x = 10S + 10x Adding S + x on both sides, F + M + S + 3x = 10S + 10x + S + x .... (This is what is what our initial equation looks like, we can now put in the value of S + x = 8 from (III) to get the value) Thus, F + M + S + 3x = 80 + 8 = 88. (1) is sufficient. 2) S + x = 2S or x = 2S - S which means that x = S. F + x = 6 (2S) or F + S= 12S or F = 11S M + x = 4(2S) or M + S= 8S or M = 7S Since no relation is mentioned between F & M, we cant find the required value. (2) is insufficient Answer is (A)

jasonfodor · Answer

Good question. You need to do two things to solve this. First set up the equation correctly, most of these are sub 600 or 600-700 level questions, second is to notice something unique with the problem (in bold below), this is what makes this a 700 level question.

Let's set up the equation. 
Let D = dad, M = mom and k = kid = son. (s looks like 5 and can be confusing so I used "k" for the son)

After reading the stem, you should set up two equations
(i) D+x=6(k+x)
(ii) M+x=4(k+x)

(1) age difference between parents is 16 years.

since is x years the dad will be 6 times older than the son, while in x years the mom will only be 4 times older than the son... this tells you the dad is older than the mom. so D = M + 16. plug this into equation (i) for D to get:
M+16+x=6(k+x) (we'll call this equation (iii))

Now, this equation (iii) should alert you that it looks a lot like equation (ii) above. The next step is to make equation (iii) look like equation (ii) so that way we can cancel out the left side. We can do this by subtracting 16 to get:

M+x= 6k + 6x - 16 (we'll call this equation iv)
M+x= 4k +4x (iii)

6k + 6x -16 = 4k +4x 
2k+2x = 16
 k+x = 8

This tells you in x years the kid/son will be 8 years old. You can plug this into equation (i) and (ii) above to get the dad's age is x years (48 years) and the mom's age in x years (32 years).  Sufficient

(2.) After 'x' years the son will be twice as old as he is now
so k + x = 2k 
k = x

You can quickly see this is insufficient by plugging in random numbers for k=x into equation (i) and (ii), for example if k = x = 1 then in x years the kid will be 2 and the dad will be 12. And if k = x = 2, then then in x years the kid will be 4 and the dad will be 24.  insufficient

aserghe1 · Answer

Such a good solution by  chetan2u

If we let y = kid's present age, and y+x = kid's age in x years, sure we can solve the problem, but it becomes unnecessarily complex.
However, if we let y = kid's age in x years (as you suggest), then the problem becomes wayyyy easier.

gmatzpractice · Answer

f+x=6(s+x)
m+x=4(s+x)

What is f+x+m+x+s+x ?

(1) f-m=16
16=2(s+x)
s+x=8 
f+x=48
m+x=32
Sum is 88
Sufficient

(2) s+x=2s
x=s
f+x=12x
m+x=8x
s+x=2x
Sum is 22x
Insufficient

Answer A

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