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

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

by swerve » Mon Sep 10, 2018 10:46 am

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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.

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

by fskilnik@GMATH » Mon Sep 10, 2018 11:22 am
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.
Last edited by fskilnik@GMATH on Tue Sep 11, 2018 8:03 am, edited 2 times in total.
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The sum of the ages of Doris and Fred is y years. If Doris i

by fskilnik@GMATH » Mon Sep 10, 2018 11:28 am
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.
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by Brent@GMATPrepNow » Mon Sep 10, 2018 3:26 pm
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

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by GMATGuruNY » Mon Sep 10, 2018 4:56 pm
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.
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by Scott@TargetTestPrep » Fri Sep 14, 2018 8:26 am
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

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