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!
Today Jim is twice as old as Fred, and Sam is 2 years
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TODAY'S AGESAAPL 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 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
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We can PLUG IN THE ANSWERS, which represent Jim's current age.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
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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We can let J, S, and F = the current age of Jim, Fred, and Sam, respectively and create the equations: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
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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