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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Jan 23, 2021 6:53 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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Source: Beat The GMAT — Problem Solving | Sat Jan 23, 2021 6:53 am

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Sat Jan 23, 2021 10:46 am

Vincen wrote: ↑
Sat Jan 23, 2021 6:53 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

Before $2x + y$ years ago:

$3x + y$

Now, $2x + y$ years after

$3x + y + 2x + y = 5x + 2y$

Now, $x$ years ago

$5x + 2y -x = 4x + 2y \Longrightarrow$ B

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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 » Thu Jan 28, 2021 6:06 am

Vincen wrote: ↑
Sat Jan 23, 2021 6:53 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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