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

Question

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

BrentGMATPrepNow · Accepted Answer

TODAY'S AGES   
  Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred.  
Let x = Fred's age TODAY
So,  2x  = Jim's age TODAY
And  x - 2  = Sam's age TODAY

AGES FOUR YEARS AGO   
Let's first determine Jim's age and Sam's age FOUR YEARS AGO
If  2x  = Jim's age TODAY, then  2x  - 4 = Jim's age FOUR YEARS AGO
If  x - 2   = Sam's age TODAY, then  x - 2   - 4 = Sam's age FOUR YEARS AGO

Four years ago Jim was 4 times as old as Sam.  
In other words, the value of  2x  - 4 is  4 times  the value of  x - 2   - 4
So, we can write:  2x  - 4 = 4( x - 2  -4)
Simplify right side: 2x - 4 = 4(x - 6)
Expand right side: 2x - 4 = 4x - 24
Add 24 to both sides: 2x + 20 = 4x
Subtract 2x from both sides: 20 = 2x
Solve: x = 10

How old is Jim NOW?   
  2x  = Jim's age TODAY
Since x = 10, we know that Jim's age = 2(10) = 20

Answer: D

Bunuel · Answer

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.

carcass · Answer

A bit tricky problem Thanks Mod for the explanation, as usual

premnath · Answer

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)    
------(2x-4)-----(x-4)-------(x-2-4)---------------------------------------

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

carcass · Answer

is pretty nice your method, it depends what is more comnfortable for you. For me is much faster in this scenario the algebric approach

PareshGmat · Answer

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

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep · Answer

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

ueh55406 · Answer

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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