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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

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

by BTGmoderatorDC » Wed Oct 10, 2018 4:39 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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Source: Beat The GMAT — Problem Solving | Wed Oct 10, 2018 4:39 pm

Ash Mo: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Oct 03, 2018 10:34 am

by Ash Mo » Sat Oct 13, 2018 11:27 am

Let R, D and S be the present ages of Richard, David and Scott respectively.
Therefore we can formulate the given equations from the data given

R=D+8
D=S+8
Also after 8 years, Richard will be twice as old as Scott, giving us the equation
R+8=(S+8)

Solving these 3 equations , we get
D=14
Thus, the age of David 4 years ago would be 10.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Sat Oct 13, 2018 2:09 pm

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
Source: Princeton Review

$$? = D - 4$$
$$R = D + 6\,\,\,\,\mathop \Rightarrow \limits^{ + \,8} \,\,\,\,\,R + 8 = D + 14\,\,\,\left( 1 \right)$$
$$D = S + 8\,\,\,\left( 2 \right)$$
$$R + 8 = 2\left( {S + 8} \right)\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right),\left( 2 \right)} \,\,\,D + 14 = 2D\,\,\,\, \Rightarrow \,\,\,\,14 = D$$
$$? = 10$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 13, 2018 5:50 pm

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

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

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