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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  [#permalink]

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New post 25 Feb 2014, 00:07
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D
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 115
Category: Algebra Applied problems; Simultaneous equations
Page: 76
Difficulty: 600


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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 25 Feb 2014, 00:07
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SOLUTION

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 sum of the ages of Doris and Fred is y years: d + f = y;
Doris is 12 years older than Fred: d = f + 12.

Subtract one from another: f = y - f - 12 --> f = y/2 - 6.

y years from now, Fred will be f + y = y/2 - 6 + y = 3y/2 - 6 years old.

Answer: D.

Similar "age" problems to practice:
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what-is-ricky-s-age-now-165766.html
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 25 Feb 2014, 02:12
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Let the ages of Fred and Doris be 'F' and 'D' respectively.

Sum of their ages = F+D = y
Now since Doris is 12 years older than Fred , D=F+12
Therefore 2F+12=y
thus F=y/2 - 6

'y' years from now Fred will be F=y/2-6+ y = 3y/2 -6

Thus answer = Option (D)
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 25 Feb 2014, 22:15
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Let the ages of Doris and Fred be D and F respectively.

Given that, D + F = y & D = F + 12;
F + 12 + F = y;
2F + 12 = y;
2F = y - 12;
F = y/2 - 6;

Now, since we are asked for Fred's age "y" years from now, we can add y to F:
F + y = y + y/2 - 6;
F + y = 3y/2 - 6;

Ans is (D).
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 26 Feb 2014, 02:06
1
Option D.
D+F=y
And D=F+12
Therefore,2F+12=y
Or F=(y-12)/2
After y years,F=y+(y-12)/2
F=3y/2-6
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 01 Mar 2014, 04:39
SOLUTION

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 sum of the ages of Doris and Fred is y years: d + f = y;
Doris is 12 years older than Fred: d = f + 12.

Subtract one from another: f = y - f - 12 --> f = y/2 - 6.

y years from now, Fred will be f + y = y/2 - 6 + y = 3y/2 - 6 years old.

Answer: D.

Similar "age" problems to practice:
today-rose-is-twice-as-old-as-sam-and-sam-is-3-years-younger-131477.html
jack-is-now-14-years-older-than-bill-if-in-10-years-jack-144435.html
age-problem-m03q13-74810.html
if-father-s-age-is-1-less-than-twice-the-son-s-age-what-is-126832.html
john-is-20-years-older-than-brian-12-years-ago-john-was-132135.html
8-years-ago-george-was-half-as-old-as-sarah-sarah-is-now-132076.html
in-ten-years-david-will-be-four-times-as-old-as-aaron-twen-104243.html
roy-is-now-4-years-older-than-erik-and-half-of-that-amount-90386.html
three-years-from-now-dathan-will-be-three-times-as-old-as-e-162041.html
if-mario-was-32-years-old-8-years-ago-how-old-was-he-x-year-164898.html
what-is-ricky-s-age-now-165766.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 13 Apr 2014, 07:10
D+F = Y ---------------------- First Equation.

D=F+12 ---------------------- Second Equation

how many years old will Fred be y years from now

can be represented as (F+Y).

As we need the answer in terms of Y , substitute Second Equation in First.

F+12+F= Y;
2F+12=Y.
2F=Y-12
F=Y-12/2;

Now F+Y in terms of Y is Y-12/2 + Y = 3Y/2 -6 ;
Hence D :)
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 13 Apr 2014, 20:34
Let age of Doris = d, then
Age of Fred = y-d .......... (1)

Doris is 12 yrs older than Fred

y-d+12 = d

2d = y+12

\(d = \frac{y}{2} + 6\) ......... (2)

Substituting value of d from (2) in (1)

\(Age of Fred = y - (\frac{y}{2} + 6)\)

\(= \frac{y}{2} - 6\)

Age of Fred after y yrs

\(=\frac{y}{2} - 6 + y\)

\(= \frac{3y}{2} - 6\)

Answer = D
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 11 Jun 2014, 14:41
It can be easily solved using smart numbers
Doris = D, Fred = F
Let's say D = 24 than F is 12 less = 12 --> 24 + 12 = Y = 36; So in Y or 36 Years Fred will be 12 + 36 = 48
Plugin 36 for Y, in a right answer you schould get 48 --> D (3*36)/2-6 = 48
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The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 09 Dec 2016, 03:46
BrainLab wrote:
It can be easily solved using smart numbers
Doris = D, Fred = F
Let's say D = 24 than F is 12 less = 12 --> 24 + 12 = Y = 36; So in Y or 36 Years Fred will be 12 + 36 = 48
Plugin 36 for Y, in a right answer you schould get 48 --> D (3*36)/2-6 = 48

I tried this method and I am completely stumped.

3*36=108
2-6=-4

108/4=27 not 48.

:shock: :?: Can somebody please explain what I am doing wrong?
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 14 Feb 2018, 17:06
Hi All,

You should notice that the answer choices all include the variable Y; they're all written "in terms of Y."

This question can be solved with Algebra or by TESTing VALUES. Here's how to TEST VALUES...

We're given two facts to work with:
1) The sum of Doris's and Fred's ages is Y
2) Doris is 12 years old than Fred

IF....
Fred = 2
Doris = 14
Y = 2+14 = 16

We're asked how old Fred will be Y years from now. Fred is now 2; in 16 years, he'll be 18. Thus, we're looking for an answer that equals 18 when Y = 16. There's only one answer that matches....

Final Answer:

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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 04 May 2018, 10:39
dheeraj24 wrote:
D+F = Y ---------------------- First Equation.

D=F+12 ---------------------- Second Equation

how many years old will Fred be y years from now

can be represented as (F+Y).

As we need the answer in terms of Y , substitute Second Equation in First.

F+12+F= Y;
2F+12=Y.
2F=Y-12
F=Y-12/2;

Now F+Y in terms of Y is Y-12/2 + Y = 3Y/2 -6 ;
Hence D :)


hello pushpitkc can you please provide explanation for this part Now F+Y in terms of Y is Y-12/2 + Y = 3Y/2 -6 ;

i dont get why we add \(y\) in denominator :? when it comes to "in terms of" i sometimes find it difficult get correct answer :)

many thanks! :)
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The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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New post 04 May 2018, 14:22
1
Hi dave13

(Q) 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?

The best method is to write equations from the question stem
D + F = y -> (1)
D = F + 12
Rewriting, D - F = 12 -> (2)

Adding (1) and (2), we will get \(2D = 12 + y\) -> \(D = 6 + \frac{y}{2}\)

Substituting this value of D in equation (1)
\(F = y - D\) = \(y - (6 + \frac{y}{2})\) = \((y - \frac{y}{2}) - 6\) = \(\frac{y}{2} - 6\)

Therefore, Fred will be \(y + (\frac{y}{2} - 6)\) = \(\frac{3y}{2} - 6\) years old, y years later.
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