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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
A bit tricky problem

Thanks Mod for the explanation, as usual :)
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
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carcass wrote:
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now?

A. 8
B. 12
C. 16
D. 20
E. 24


Use of graphical presentation helps a lot in such age related questions. Let's see how it works.

----------4 yeas ago----------------------------today------------
-------J-------F--------S---------------------.J---------F---------S

----------------------------------------------(2x)--------(x)---------(x-2) [let's consider today age of Fred is x, the ages of Jim is 2x, and age of Sam is (x-2)]
------(2x-4)-----(x-4)-------(x-2-4)---------------------------------------[this are the ages of J, F and S 4 years ago]


As, per condition given in the question,
->2x-4= 4(x-6)
-> 2x-4=4x-24
-> 20=2x
-> x=10

Therefore, 2x=20, this is the age of Jim today.
So, the answer is D
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
premnath wrote:
carcass wrote:
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now?

A. 8
B. 12
C. 16
D. 20
E. 24


Use of graphical presentation helps a lot in such age related questions. Let's see how it works.

----------4 yeas ago----------------------------today------------
-------J-------F--------S---------------------.J---------F---------S

----------------------------------------------(2x)--------(x)---------(x-2) [let's consider today age of Fred is x, the ages of Jim is 2x, and age of Sam is (x-2)]
------(2x-4)-----(x-4)-------(x-2-4)---------------------------------------[this are the ages of J, F and S 4 years ago]


As, per condition given in the question,
->2x-4= 4(x-6)
-> 2x-4=4x-24
-> 20=2x
-> x=10

Therefore, 2x=20, this is the age of Jim today.
So, the answer is D


is pretty nice your method, it depends what is more comnfortable for you.

For me is much faster in this scenario the algebric approach ;)
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
Jim ................ Fred ....................... Sam

a-4 .................................................. \(\frac{1}{2}a - 4 - 2\) (Ages 4 years ago)


a ....................... \(\frac{1}{2} a\) .......................... \(\frac{1}{2} a - 2\) (Current Ages)

\(a-4 = 4(\frac{1}{2}a - 6)\)

a = 20

Answer = D
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
Expert Reply
Hi All,

This question can be solved by TESTing THE ANSWERS and doing a bit of arithmetic:

We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Four years ago, Jim was 4 times as old as Sam.

Let's TEST Answer B: 12

IF....Jim is currently 12 years old....
Fred is 6 years old
Sam is 4 years old
4 years ago, Jim was 8 and Sam was 0, so Jim was NOT 4 times as old as Sam. We need Sam to be OLDER, so everyone else has to be older too.
Eliminate Answers A and B.

Next, let's TEST Answer D: 20

IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
4 years ago, Jim was 16 and Sam was 4, so Jim WAS 4 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
Expert Reply
carcass wrote:
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now?

A. 8
B. 12
C. 16
D. 20
E. 24


We can let J, S, and F = the current age of Jim, Fred, and Sam, respectively and create the equations:

J = 2F

And

S = F - 2

S + 2 = F

And

J - 4 = 4(S - 4)

J - 4 = 4S - 16

J = 4S - 12

Since J = 2F we have:

2F = 4S - 12

F = 2S - 6

Since S + 2 = F, we have:

S + 2 = 2S - 6

8 = S, so J = 4 x 8 - 12 = 20.

Answer: D
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
Today their ages are as follows:
Fred: F
J=2F
S= F-2

4 years ago. (Do remember to subtract 4 years from both the ages, I for one, somehow forget this step.)

Jim's age-4 and Sam's age-4 >> Jim: 2F-4 and Sam: F-2-4

As per the question: Jim's age is 4 times Sam's age

2F-4= 4*(F-2-4)

we need to find 2F (look above, 2F Jim's age today)
2F= 4F-8-16+4
2F=20.
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]
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