• 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

The sum of the ages of Doris and Fred is y years. If Doris

This topic has 5 expert replies and 0 member replies

The sum of the ages of Doris and Fred is y years. If Doris

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6

The OA is D.

Source: Official Guide

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
swerve wrote:
The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
Source: Official Guide
Now Algebra!!
\[?\,\,\,:\,\,\,\,F + y\,\, = \,\,f\left( y \right)\]
\[\left\{ \begin{gathered}
\left( 1 \right) \hfill \\
\left( 2 \right) \hfill \\
\end{gathered} \right.\begin{array}{*{20}{c}}
{\,D + F = y} \\
{\,D - 12 = F}
\end{array}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,F + 12 = y - F\,\,\,\,\, \Rightarrow \,\,\,\,\,2F = y - 12\]
\[?\,\,\,:\,\,\,F + y\,\,\, = \,\,\,\left( {\frac{y}{2} - 6} \right) + y\,\,\, = \,\,\,\frac{{3y}}{2} - 6\]
This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag
Post
swerve wrote:
The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
Source: Official Guide
Let´s explore a particular case!
D (Doris now) = 13 years
F (Fred now) = 1 year
(Doris is 12 years older than Fred!)
y = D+F = 14
Target answer: ? = F+y = 15 (years)...

(A) y-6 = 15-6 NO
(B) 2y-6 = 28-6 NO
(C) y/2 - 6 = 1 NO
(D) 3y/2 - 6 = 21-6 = 15 YES (this one "survives"!)
(E) 5y/2 - 6 obviously not equal to (D) ... NO

We were "lucky": only one survivor means the survivor IS the right answer...

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

Regards,
fskilnik.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!



Last edited by fskilnik@GMATH on Tue Sep 11, 2018 8:03 am; edited 2 times in total

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
swerve wrote:
The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
Let F = Fred's PRESENT age

Doris is 12 years older than Fred.
In other words, Doris' age = F + 12.
So, the sum of their ages = F + (F + 12)
Simplify to get: sum of their ages = 2F + 12

The sum of the ages = y
2F + 12 = y

Now solve for Fred's age (F).
Start with: 2F + 12 = y
Subtract 12 form both sides: 2F = y - 12
Divide both sides by 2 to get: F = (y - 12)/2
Rewrite as: F = y/2 - 12/2
Simplify: F = y/2 - 6
So, Fred's PRESENT age is y/2 - 6

How many years old will Fred be y years from now, in terms of y?
Add y to Frank's PRESENT age to get: y/2 - 6 + y

Check the answer choices . . . y/2 - 6 + y isn't there!
Looks like we need to SIMPLIFY

y/2 - 6 + y = y/2 - 6 + 2y/2 (get common denominator of 2)
= 3y/2 - 6
= D

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post
swerve wrote:
The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
Since Doris is 12 years older than Fred, let Fred = 2 and Doris = 2+12 = 14.
y = sum of their ages = 2+14 = 16.
Since Fred = 2 and y=16, Fred's age y years from now = 2+16 = 18. This is our target.
Now plug y=16 into the answers to see which yields the target value of 18.
Only D works:
3y/2 - 6 = 3(16/2) - 6 = 24 - 6 = 18.

The correct answer is D.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
swerve wrote:
The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
We can let Doris’s age today = d and Fred’s age today = f and create the following equations:

d + f = y

and

d = 12 + f

Substituting, we have:

12 + f + f = y

2f = y - 12

f = (y - 12)/2

So y years from now Fred will be:

(y - 12)/2 + y = (y - 12)/2 + 2y/2 = (3y - 12)/2 = 3y/2 - 6

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 Brent@GMATPrepNow 67 first replies
2 fskilnik@GMATH 53 first replies
3 Jay@ManhattanReview 39 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 31 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

128 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 image description Max@Math Revolution

Math Revolution

88 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

78 posts
5 image description Jay@ManhattanReview

Manhattan Review

75 posts
See More Top Beat The GMAT Experts