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) EDITIONGRE - 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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Brent Hanneson - founder of Greenlight Test Prep