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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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24 Feb 2014, 23:07
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Difficulty:

55% (hard)

Question Stats:

65% (01:26) correct 35% (01:36) wrong based on 902 sessions

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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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24 Feb 2014, 23:07
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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.

Similar "age" problems to practice:
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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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25 Feb 2014, 01:12
3
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

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

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25 Feb 2014, 21:15
2
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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26 Feb 2014, 01:06
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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01 Mar 2014, 03:39
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.

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

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13 Apr 2014, 06:10
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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13 Apr 2014, 19:34
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

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

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

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

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11 Jun 2014, 13:41
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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09 Dec 2016, 02:46
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.

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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14 Feb 2018, 16:06
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....

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

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04 May 2018, 09:39
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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04 May 2018, 13:22
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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Re: The sum of the ages of Doris and Fred is y years. If Doris  [#permalink]

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18 Dec 2018, 22:31
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.
Re: The sum of the ages of Doris and Fred is y years. If Doris &nbs [#permalink] 18 Dec 2018, 22:31
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