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Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If

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Bunuel
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Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   17 Oct 2017, 23:31
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Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

(A) 5
(B) 10
(C) 13
(D) 16
(E) 18
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C
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ewmike
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   18 Oct 2017, 02:27
Let jim daughter be d
Jim son be x
X-8=2d-8
X=d+5
d+5-8=2d-8
d-3=2d-d
d=5
A is correct

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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   18 Oct 2017, 02:39
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EQ 1 Jim's son = S
Jim's Daughter = D

(S-8)= 2 (D-8)
S-8 = 2D- 16
S-2D= -8
EQ2 S= D+5 or S- D = 5

Equating eq 1 and 2

D=13
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   18 Oct 2017, 11:16
s=son's age now
d=daughter's age now

(s-8)/(d-8)=2
s-d=5

solve about equations:
d=13 (C)

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Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   18 Oct 2017, 15:09
Expert Reply
Bunuel wrote:
Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

(A) 5
(B) 10
(C) 13
(D) 16
(E) 18

Exactly 8 years ago, Jim’s son, S, was twice as old as Jim’s daughter, D

S - 8 = 2(D - 8)

Son is now five years older than daughter:

S = D + 5
Substitute for S in first equation

(D + 5) - 8 = 2(D - 8)
D - 3 = 2D - 16
D = 13

(Check: D is 13 now; 8 years she ago was 5. S is 18 now (= D + 5), so 8 years ago he was 10. 10 = twice as old as 5, back then. Correct.)

Answer C
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   19 Oct 2017, 03:47
ewmike wrote:
Let jim daughter be d
Jim son be x
X-8=2d-8
X=d+5
d+5-8=2d-8
d-3=2d-d
d=5
A is correct



Hi,
There is an errot here. You did not mulyply 2 * 8 too. it should be

2 (d -8) = 2d - 16
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   23 Oct 2017, 11:11
-I set the original equation up as (s-8)=2(d-16), which simplifies to s-8=2d-16.
-we are given s=d+5, so I substitute that in for s.
-d-3=2d-16, simplified d=13.

Initially, I made a small mistake and got d=5, quickly checking my math, I realized the daughter cannot be 5 because 8 years ago she wasn't born yet. So I redid it until I figured out my mistake. I wasted a lot of time on something pretty simple here.

Simple mistakes are my biggest problem, I know the material pretty well, but I just make a lot of dumb errors. Any guidance would be appreciated.
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   23 Oct 2017, 11:55
If Son = X
Daughter=X-5

EQ: x-8=2(X-5-8)
X-8=2X-26
X=18

Daughter = 18-5= 13

Answer is C
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   24 Oct 2017, 06:06
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Bunuel wrote:
Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

(A) 5
(B) 10
(C) 13
(D) 16
(E) 18


We can let Jim’s son’s current age = s and Jim’s daughter’s current age = d. We can also state that 8 years ago, his son was (s - 8) years old and his daughter was (d - 8) years old. We can create the following equation:

s - 8 = 2(d - 8)

s - 8 = 2d - 16

s = 2d - 8

and

s = 5 + d

Thus:

2d - 8 = 5 + d

d = 13

Answer: C
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Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   26 Oct 2017, 03:49
we can also check from answer choices if we are unable to form the equation.
Start from C
Let Jim's daughter's age be 13 today
Jim's son age today will be 13+5=18
Now 8 years ago the son was 2 times the age of the daughter.
find the age of both of them 8 years ago
Daughter=13-8=5
Son=18-8=10
Now 10 =2x5=10=Answer C
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BrentGMATPrepNow
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   28 Aug 2018, 06:56
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Bunuel wrote:
Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

(A) 5
(B) 10
(C) 13
(D) 16
(E) 18


Jim’s son is now 5 years older than his daughter
Let D = the daughter's age NOW
So D + 5 = the son's age NOW

This also means that D - 8 = the daughter's age EIGHT YEARS AGO
This also means that D + 5 - 8 = the son's age EIGHT YEARS AGO
Or we can say, D - 3 = the son's age EIGHT YEARS AGO

8 years ago, Jim’s son was twice as old as Jim’s daughter.
8 years ago, the daughter's age was D - 8 and the son's age was D - 3
So, we can write: D - 3 = 2(D - 8)
Expand right side to get: D - 3 = 2D - 16
Solve to get D = 13

Since D = the daughter's present age, the correct answer is C

Cheers,
Brent
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Re: Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If [#permalink] New post   28 Aug 2018, 07:11
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Bunuel wrote:
Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

(A) 5
(B) 10
(C) 13
(D) 16
(E) 18

\(? = D\)

\(\left\{ \begin{gathered}\\
\left( {S - 8} \right) = 2\left( {D - 8} \right) \hfill \\\\
S = D + 5 \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\, \sim \,\,\,\,\,\,\,\left\{ \begin{gathered}\\
\left( {S - 8} \right) = 2\left( {D - 8} \right) \hfill \\\\
\left( {S - \underline 8 } \right) = \left( {D - \underline 8 } \right) + 5 \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {\, - \,} \right)} \,\,\,\,\,\,\,\,\left( {D - 8} \right) - 5 = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = D = 13\)

The above follows the notations and rationale taught in the GMATH method.
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Re: Exactly 8 years ago, Jims son was twice as old as Jims daughter. If [#permalink] New post   01 Dec 2022, 07:33
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Re: Exactly 8 years ago, Jims son was twice as old as Jims daughter. If [#permalink]
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