Today Jim is twice as old as Fred, and Sam is 2 years younge : GMAT Problem Solving (PS)
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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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12 Sep 2012, 02:44
00:00

Difficulty:

15% (low)

Question Stats:

79% (02:33) correct 21% (02:22) wrong based on 100 sessions

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

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12 Sep 2012, 02:52
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]

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12 Sep 2012, 03:14
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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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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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]

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12 Sep 2012, 10:02
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]

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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]

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04 Dec 2015, 10:58
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younge [#permalink]

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05 Dec 2015, 10:50
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.

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.

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.

[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, 10:50
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