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# Today Jim is twice as old as Fred, and Sam is 2 years younge

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Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]  12 Sep 2012, 02:44
Expert's post
00:00

Difficulty:

15% (low)

Question Stats:

88% (02:15) correct 12% (02:08) wrong based on 41 sessions
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
[Reveal] Spoiler: OA

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Kudos [?]: 40998 [0], given: 5654

Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]  12 Sep 2012, 02:52
Expert's post
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?

8
12
16
20
24

Today Jim is twice as old as Fred --> J=2F;
Today Sam is 2 years younger than Fred --> S+2=F;
Four years ago Jim was 4 times as old as Sam --> J-4=4*(S-4);

Substitute F: J=2(S+2) and J-4=4*(S-4) --> J=2S+4 and J=4S-12 --> subtract one from another 0=2S-16 --> S=8 --> J=2(S+2)=20.

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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]  12 Sep 2012, 03:14
Expert's post
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]  12 Sep 2012, 09:27
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.
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Posts: 2587
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Kudos [?]: 3372 [0], given: 720

Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]  12 Sep 2012, 10:02
Expert's post
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.

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]  24 Nov 2014, 00:22
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

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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge   [#permalink] 24 Nov 2014, 00:22
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