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

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Carcass
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Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre [#permalink] New post   13 Apr 2021, 05:54
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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

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre [#permalink] New post   13 Apr 2021, 06:18
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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?

A. 8
B. 12
C. 16
D. 20
E. 24

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book

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
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre [#permalink] New post   13 Apr 2021, 10:28
Jim is twice as old as Fred = J=2F
Sam is 2 years younger = F-2 = S
Four years ago Jim was 4 times as old as Sam= J-4=4*(S-4)----- eq1

Subsitiute the value of S in the equation- 1
J-4 = 4*(F - 2 - 4)
J-4 = 4F - 24
J = 4F - 20...... eq 2

Substitute the value of J as 2F in eq 2
2F = 4F - 20
20= 2f
10= F

2F = Jim's age TODAY
2(10) = 20


Answer: D.
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre [#permalink] New post   08 Sep 2023, 12:17
J = 2F
S = F -2
(J-4) = 4(S-4)
J-4 = 4(F-2-4)
J-4 = 4(J/2-6)
J-4 = 2J-24
-J = -20
J = 20
Choice D
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gmatclubot
Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre [#permalink]
08 Sep 2023, 12:17
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