• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has 2 expert replies and 1 member reply

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

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



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

  • +1 Upvote Post
  • Quote
  • Flag

Top Member

Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Post
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 :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

  • +1 Upvote Post
  • Quote
  • Flag
Post
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

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Top First Responders*

1 fskilnik@GMATH 76 first replies
2 Brent@GMATPrepNow 52 first replies
3 Jay@ManhattanReview 46 first replies
4 GMATGuruNY 39 first replies
5 Rich.C@EMPOWERgma... 32 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

198 posts
2 image description Scott@TargetTestPrep

Target Test Prep

177 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

134 posts
4 image description Max@Math Revolution

Math Revolution

92 posts
5 image description GMATGuruNY

The Princeton Review Teacher

86 posts
See More Top Beat The GMAT Experts