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Word Problems

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by swerve » Wed Aug 12, 2020 10:05 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

\(2x + y\) yeas 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. \(6x+y\)

The OA is B

Source: Magoosh
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Re: Word Problems

by Brent@GMATPrepNow » Wed Aug 12, 2020 12:37 pm
swerve wrote: ↑
Wed Aug 12, 2020 10:05 am
 \(2x + y\) yeas 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. \(6x+y\)

The OA is 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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Re: Word Problems

by Scott@TargetTestPrep » Sat Aug 15, 2020 3:53 am
swerve wrote: ↑
Wed Aug 12, 2020 10:05 am
 \(2x + y\) yeas 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. \(6x+y\)

The OA is 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

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