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

Question

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

Bunuel · Accepted Answer

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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Manofsteel · Answer

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)

nutshell · Answer

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).

AKG1593 · Answer

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

dheeraj24 · Answer

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

PareshGmat · Answer

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

BrainLab · Answer

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

gracie90 · Answer

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?

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

dave13 · Answer

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!

pushpitkc · Answer

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.

Krabhay · Answer

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.

Kinshook · Answer

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

sagargoyal · Answer

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 ?

Pritishd · Answer

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

MathRevolution · Answer

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

VarunPandey · Answer

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

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Basshead · Answer

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.

MyNameisFritz · Answer

Here is my explenation for "dummies" like me

Lets say Doris is 14 and Fred is 2.
Both of their ages together is 16 (or y, in this case)

In y years, how old will Fred be? 16 + 2 = 18

We need to find the answer which equals 18.

After plugging in the numbers, D is the right choice.

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

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

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