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

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

by BTGmoderatorDC » Wed Jun 26, 2019 7:59 pm

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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

OA B

Source: Princeton Review
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by deloitte247 » Thu Jul 04, 2019 5:05 am
Let Richard's age = r, David's age = d, and Scott's age = s.
$$r=d+6$$
$$d=s+8$$
In 8 years, 'r' will be twice as old as Scott
$$r+8=2\left(s+8\right)$$
$$r+8=2s+16$$
$$r=2s+8$$
$$Recall\ that,\ r=d+6,\ where\ d=s+8$$
$$r=s+8+6=s+14$$
$$where,\ r=2s+8$$
$$2s+8=s+14$$
$$s=6$$
$$r=20$$
$$and\ d=14$$
$$David's\ age\ 4\ years\ ago=>d-4$$
$$=14-4=10\ years\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(Answer=Option\ B\right)$$
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by swerve » Thu Jul 04, 2019 11:10 am
\(R\) 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 \(= S+8+14 = S+22\) (the difference will always be \(14\) years as long as both are alive)
Given: \(S+22 = 2 \cdot (S+8)\)
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 (the difference between their ages would have been same then as now)

Hence, the correct answer is B
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by Brent@GMATPrepNow » Thu Jul 04, 2019 11:42 am
BTGmoderatorDC wrote: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

OA B

Source: Princeton Review
We can also solve this with 1 variable

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
Brent Hanneson - Creator of GMATPrepNow.com
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