The sum of the ages of Doris and Fred is y years. If Doris is 12 years : Problem Solving (PS)

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

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 is 12 years [#permalink]

26 Feb 2014, 02:06

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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 is 12 years [#permalink]

01 Mar 2014, 04:39

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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.

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

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 is 12 years [#permalink]

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 is 12 years [#permalink]

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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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

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 is 12 years [#permalink]

14 Feb 2018, 17:06

Expert Reply

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:

Show Spoiler

D

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

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!

L

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

04 May 2018, 14:22

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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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

18 Dec 2018, 23:31

Statement 1. We don’t know the value of ‘y’ and the age of Doris or Fred. Hence, Insufficient.
Statement 2. We don’t know the value of ‘y’ so we can’t calculate the age of Fred. Hence, Insufficient.
Statement 1 & 2 together. (F +D) = ( F + F + 12) = y
2F + 12 = y. Since, we don’t know the value of y we cannot calculate the age of Fred. Hence, Insufficient.

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The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

08 Oct 2019, 09:35

Bunuel 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

PS68602.01

Let the ages of Doris and Fred be d & f years now

d + f = y
d = f + 12
2f + 12 = y
f = y/2 - 6

Fred's ages y years from now
f + y = 3y/2 -6

IMO D

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

12 May 2020, 00:40

I got the option C as the answer ? Below is my reasoning -
Fred's age is x and Doris age is x+12 hence, x+x+12 = y (today)
after y years, the equation will become - (x+y)+(x+12+y) = y + 2y
which will get the x value to be x = y/2 -6 (option C)
Can someone explain where am I going wrong in this ?

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

14 Aug 2020, 08:00

Bunuel 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
PS68602.01

1. Let the current ages of Doris and Fred be $D$ and $F$
2. As per the first sentence we get $D + F = y$
3. As per the second sentence we get $D = F + 12$
4. We are asked to find $F + y$ in terms of y. So, we need to replace $F$ with an expression that exclusively contains $y$

Plugging in 3 into 2 :-
$F + 12 + F = y$
$2F = y - 12$
$F = \frac{y - 12}{2}$

Plugging this value of $F$ in $F + y$ :-
$\frac{y - 12}{2} + y$

$\frac{y - 12 + 2y}{2}$

$\frac{3y - 12}{2}$

$\frac{3y}{2} - 6$

Ans D

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

15 Aug 2020, 08:58

Expert Reply

The sum of the ages of Doris and Fred is y : D + F = y

Doris is 12 years older than Fred: D - F = 12

Solving both the equations, we get 2D = 12 + y

Or, D = 6 + $\frac{y}{2}$

6 + $\frac{y}{2}$ - F = 12.

=> F = -6 + $\frac{y}{2}$

Age of Fred y years from now: F + y.

=> -6 + $\frac{y}{2}$ + y

=> $\frac{-12 + y + 2y }{ 2}$

=> $\frac{-12+ 3y }{ 2}$

=> $\frac{3y}{2}$ - 6

Answer D

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

12 Oct 2020, 19:31

D+F=Y,——eq1
D-F=12,——eq2

Eq(1-2)
2F=Y-12
Or
F=Y/2-6
After y years,
F+Y= Y/2-6+Y ( added y both side)
After equating ;
3/2Y-6

Posted from my mobile device

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

12 Nov 2020, 13:17

$d + f = y$
$d = f + 12$
$f + 12 + f = y$
$2f + 12 = y$
$f = y - \frac{12 }{ 2}$
$f = \frac{y}{2} - 6$

In y years, $f = \frac{3y}{2} - 6$

Answer is D.

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Re: The sum of the ages of Doris and Fred is y years. If Doris is 12 years [#permalink]

12 Nov 2020, 13:17

GMAT Problem Solving (PS) Questions

The sum of the ages of Doris and Fred is y years. If Doris is 12 years