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

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Bunuel
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2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 02:51
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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
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B
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 03:19
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Bunuel wrote:
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


2x + y years ago, Roberto was 3x + y years old, so today he will be (3x+y) + 2x+y = 5x + 2y years old.

So, x years ago from today, Roberto was (5x+2y) - x = 4x + 2y years old.

Hence Option (B) is our choice.

Best,
GLadi
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 03:58
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The solution can be best demonstrated in a table.

If he was 3x+y years old, 2x+y years ago.

The now he will be \(3x + y + 2x + y = 5x + 2y\)

X years ago is basically 5x + 2y - x = 4x + 2y

Answer choice B
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 06:11
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Now, Roberto is (3x+y) + (2x + y) = 5x + 2y years old
x years ago, he was 5x+2y - x = 4x + 2y years old.

Hence Option B.

Now, another way is to plug in numbers, say x = 1, y = 1.

So, 2*1 + 1 = 3 years ago Roberto was 3*1 + 1 = 4 years old. So, now, Roberto is 4+3 = 7 years old, x = 1 year ago, he was 6 years old. Check options now.
A: 1, Incorrect
B: 6, Correct
C: 7, Incorrect
D: 8, Incorrect
E: 7, Incorrect

Hence Option B again!
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 06:22
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Bunuel wrote:
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


OA: B

Let current age be \(z\)

According to Question,
\(z-(2x+y)=3x+y\)
\(z=5x+2y\).........(1)

Age of Roberto \(x\) years ago\(= z-x=5x+2y-x=4x+2y\)
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BrentGMATPrepNow
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2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   Updated on: 28 Jan 2021, 07:05
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Bunuel wrote:
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


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

Originally posted by BrentGMATPrepNow on 17 Oct 2018, 06:25.
Last edited by BrentGMATPrepNow on 28 Jan 2021, 07:05, edited 1 time in total.
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Oct 2018, 13:35
Bunuel wrote:
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



After 2x + y :

3x + y + 2x + y = 5x + 2y.

Before x years ago;

5x + 2y - x = 4x + 2y .

The best answer is B.
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   18 Oct 2018, 18:18
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Bunuel wrote:
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


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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BrentGMATPrepNow
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   09 Sep 2020, 07:17
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Top Contributor
Bunuel wrote:
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

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
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Rogermoris
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   09 Sep 2020, 07:56
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\(2x + y\) years ago Roberto was \(3x + y\) years old

Say, 4 years ago, you were 20 years ago, which simply means today you are 24 years old (4+20)

Hence, Today he will be \((3x+y) + 2x+y = 5x + 2y\) years old.

So, x years ago from today, Roberto was \((5x+2y) - x = 4x + 2y\) years old.

Which is Option [B]
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink] New post   17 Jan 2021, 12:25
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Bunuel wrote:
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

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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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was [#permalink]
17 Jan 2021, 12:25
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