Jim is twice as old as Fred ...

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Mon Dec 24, 2007 4:34 pm

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 ?

What is the best and quickest way to work this out ?

Thanks.
II

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Source: Beat The GMAT — Problem Solving | Mon Dec 24, 2007 4:34 pm

sujaysolanki: Master | Next Rank: 500 Posts; Posts: 214; Joined: Wed Nov 14, 2007 6:30 am; Thanked: 15 times

by sujaysolanki » Tue Dec 25, 2007 11:43 pm

Jim 2x
Fred x
Sam x-2

Four years ago
2x - 4 = 4(x-2-4)
x comes to 10
So Jim should be 20

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preciousrain7: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Dec 06, 2007 4:16 pm; Location: NYC, NY; Thanked: 2 times

by preciousrain7 » Thu Dec 27, 2007 3:53 pm

sujaysolanki wrote:Jim 2x
Fred x
Sam x-2

Four years ago
2x - 4 = 4(x-2-4)
x comes to 10
So Jim should be 20

I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Thu Dec 27, 2007 7:08 pm

preciousrain7 wrote:
sujaysolanki wrote:Jim 2x
Fred x
Sam x-2

Four years ago
2x - 4 = 4(x-2-4)
x comes to 10
So Jim should be 20
I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?

Thats a good point ! I understood it to be Sam's age 4 years ago.

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Thu Dec 27, 2007 10:24 pm

I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?

preciousrain7, it should be compared with Sam's age 4 years ago otherwise it will be mentioned in the Qs to compare Jim's age 4yrs ago with Sam's current age!

Correct me If I am wrong

Regards,

Amitava

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jun 13, 2019 6:20 am

I've added the answer choices....

II wrote: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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Jun 17, 2019 4:27 pm

II wrote: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 ?

What is the best and quickest way to work this out ?

Thanks.
II

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.

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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