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

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by AAPL » Fri Jun 01, 2018 5:02 am
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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

The OA is D.

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.

Has anyone another strategic approach to solve this PS question? Regards!
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by Brent@GMATPrepNow » Fri Jun 01, 2018 5:29 am
AAPL 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
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Jim, Fred and Sam

by GMATGuruNY » Fri Jun 01, 2018 5:52 am
AAPL 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 PLUG IN THE ANSWERS, which represent Jim's current age.
When the correct answer is plugged in, Jim's age four years ago will be 4 times Sam's age four years ago.

B: J=12
Since Jim is twice as old as Fred, F=6.
Since Sam is 2 years younger than Fred, S=4.
Four years ago, J = 12-4 = 8 and S = 4-4 = 0.
Since Sam's age four years ago must be positive, all of the ages must increase in value.
Thus, a bigger answer choice is needed.
Eliminate A and B.

D: J=20
Since Jim is twice as old as Fred, F=10.
Since Sam is 2 years younger than Fred, S=8.
Four years ago, J = 20-4 = 16 and S = 8-4 = 4.
Success!
Jim's age four years ago is 4 times Sam's age four years ago.

The correct answer is D.
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by Jeff@TargetTestPrep » Sun Jun 03, 2018 5:27 pm
AAPL 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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Head of GMAT Instruction
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