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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]

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New post 12 Sep 2012, 03:44
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (02:25) correct 17% (02:11) wrong based on 68 sessions

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

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New post 12 Sep 2012, 03:52
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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?

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.

Answer: D.
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]

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New post 12 Sep 2012, 04:14
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]

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New post 12 Sep 2012, 10:27
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.
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]

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New post 12 Sep 2012, 11:02
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.
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]

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New post 24 Nov 2014, 01:22
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

Answer = D
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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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New post 05 Dec 2015, 11:50
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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:
[Reveal] Spoiler:
D


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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge   [#permalink] 05 Dec 2015, 11:50
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