\(2x + y\) 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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Brent@GMATPrepNow
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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
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Scott@TargetTestPrep
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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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