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

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

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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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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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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