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Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre
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13 Apr 2021, 05:54
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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
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Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre
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13 Apr 2021, 06:18
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
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
Re: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fre
[#permalink]
13 Apr 2021, 10:28
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.
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.
