2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Wed Jan 06, 2021 8:00 am

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2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

A. x
B. 4x + 2y
C. 5x + 2y
D. 6x + 2y
E. 6x + y

Answer: B
Source: Magoosh

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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

by Scott@TargetTestPrep » Fri Jan 15, 2021 10:24 am

BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:00 am
2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

A. x
B. 4x + 2y
C. 5x + 2y
D. 6x + 2y
E. 6x + y

Answer: B

Solution:

We can let r = Roberto’s age today and create the equation:

r - (2x + y) = 3x + y

r - 2x - y = 3x + y

r = 5x + 2y

We see that Roberto is currently (5x + 2y) years old. So x years ago, he was 5x + 2y - x = 4x + 2y years old.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
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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

Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

by Brent@GMATPrepNow » Sat Jan 16, 2021 6:55 am

BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:00 am
2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?

A. x
B. 4x + 2y
C. 5x + 2y
D. 6x + 2y
E. 6x + y

Answer: B
Source: Magoosh

Let R = Roberto's PRESENT age.
So, R - x = Roberto's age X YEARS AGO (this is our goal!)
Also, R - (2x + y) = Roberto's age (2x + y) YEARS AGO

2x + y years ago, Roberto was 3x + y years old.
We can write: R - (2x + y) = 3x + y
Remove brackets: R - 2x - y = 3x + y
Add y to both sides to get: R - 2x = 3x + 2y
Add x to both sides to get: R - x = 4x + 2y

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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