A certain family has 3 sons: Richard is 6 years older than David, and

Question

A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

GMATinsight · Answer

Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"

Now 
Richard is 6 years older than David,
i.e. R = D +6

David is 8 years older than Scott
i.e. D = S +8

If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8

But R = D+6 = (S+8)+6 = S+14

therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14

Now,
 how old was David 4 years ago?

i.e. D-4 = 14-4 = 10 years

Answer: Option  B

amanvermagmat · Answer

R is 6 years older than D, D is 8 years older than S
So R is (6+8)=14 years older than S, so we can say that R = S + 14

After 8 years, age of Scott = S+8, age of Richard = S+8+14 = S+22 (difference will always be 14 years as long as both are alive)
Given: S+22 = 2*(S+8) 
Solve to get S=6

Thus currently S is 6 years, 4 years ago S would have been 2 years old, and David must have been 2+8 = 10 years old (difference between their ages would have been same then as now)

Hence answer is  B

Manick9 · Answer

You shd draw a model to visualize their ages.

Scott + 14 + 8 = 2 (Scott + 8)
Scott = 6 years
David = 14 years.
4 years ago, David was 10 years old.

Answer : B

ScottTargetTestPrep · Answer

We can create the equations:

R = D + 6

and

D = S + 8

So we have R = (S + 8) + 6 or R = S + 14. We are also given that in 8 years, Richard will be twice as old as Scott. We express Richard’s age in 8 years as (R + 8) and Scott’s age in 8 years as (S + 8), so we have:

R + 8 = 2(S + 8)

S + 14 + 8 = 2S + 16

6 = S

Therefore, Scott is currently 6 years old and David is 6 + 8 = 14 years old. So 4 years ago, David was 10 years old.

Answer: B

energetics · Answer

Drawing a table for this helps a lot. Solving with 1 variable:

"Richard is 6 years older than David, and David is 8 years older than Scott."

NOW 
R= x+6
D= x
S= x-8

+8 years 
R= x+14
D= x+8
S= x

"If in 8 years, Richard will be twice as old as Scott" 
x+14 = 2x
x = 14

"how old was David 4 years ago?"
David is NOW x, or 14 years old so 14-4 = 10, B

BrentGMATPrepNow · Answer

David is 8 years older than Scott  
Let x = Scott's age NOW
So, x + 8 = David's age NOW

Richard is 6 years older than David  
If x + 8 = David's age NOW, then...
(x + 8) + 6 = Richard's age NOW
In other words, x + 14 = Richard's age NOW

In in 8 years, Richard will be twice as old as Scott  
IN 8 YEARS, Scott's age =  x + 8 
IN 8 YEARS, Richard's age = (x + 14) + 8 =  x + 22

We can write: (Richard's age IN 8 YEARS) = 2(Scott's age IN 8 YEARS) 
In other words,  x + 22  = 2( x + 8 )
Expand: x + 22 = 2x + 16
Solve: x = 6

How old was David 4 years ago?  
We know that x + 8 = David's age NOW
Since we now know that x = 6, David's age NOW = 6 + 8 = 14
So, 4 YEARS ago, David's age = 14 - 4 = 10

Answer: B

Cheers,
Brent

bumpbot · Answer

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A certain family has 3 sons: Richard is 6 years older than David, and

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