Ages of Ebo and Atu

[Pazoki]

Below is a question by GMAT Prep Now.

5 years ago, Ebo was 3 times as old as Atu. In 3 years Ebo will be twice as old as Atu. What is the sum of their ages now?

A) 18
B) 24
C) 28
D) 35
E) 42

Brent solved it based on 2 variable and 2 equations. I solved it with on variable but not sure my way is valid or not. thank for any hint or guidance.

I got Aut as he/she is younger. So Ebo in 5 yaers ago is 3(A-5) and when we add 8 years to it we will get 3 years from now which will be 3(A-5)+8=2(A+3) ==> 3A-7=2(A+3),solved for "A" and got A=13, then plug "A" in in the equation to solve for Ebo or E=29 then E+A=> 29+13=42 (E) is correct.
Did I do correctly?

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Hi Pazoki,

Yes, your approach is correct. You're going to find that most GMAT questions can be solved in a variety of ways (and there are even various ways of 'doing math' that will get you to the correct answer). Ultimately, you should be honing all of your skills so that you can choose whichever approach is fastest and easiest for you on Test Day (instead of ending up 'stuck' with just one approach because you didn't practice the others).

Relative to using two variables, was this approach easier? Was it faster? Did you have to go back and reread the prompt repeatedly while you were working through your calculations? These are relevant questions to consider. Getting the correct answer is important, but doing so in an efficient fashion is also important.

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

5 years ago, Ebo was 3 times as old as Atu. In 3 years, Ebo will be twice as old as Atu. What is the sum of their ages now?

A) 18
B) 24
C) 28
D) 35
E) 42

An alternate approach is to TEST CASES.

5 years ago, Ebo was 3 times as old as Atu.
What is the sum of their ages now?

Case 1: Five years ago A=1 and E = 3*1 = 3
Sum of the their ages now = (1+5) + (3+5) = 14.
14 is not among the answer choices.

Case 2: Five years ago A=2 and E = 3*2 = 6
Sum of the their ages now = (2+5) + (6+5) = 18.
In 3 years, A = 7+3 = 10 and E = 11+3 = 14.
Since Ebo is not twice as old as Atu, eliminate A.

Case 3: Five years ago A=3 and E = 3*3 = 9
Sum of the their ages now = (3+5) + (9+5) = 22.
22 is not among the answer choices.

Notice the PATTERN:
The resulting sums -- 14, 18, 22 -- keep increasing by 4.
Thus, the correct sum must be in the following list:
14, 18, 22, 26, 30, 34, 38, 42...

Only the value in red is among the remaining answer choices.

The correct answer is E.

[Pazoki]

5 years ago, Ebo was 3 times as old as Atu. In 3 years, Ebo will be twice as old as Atu. What is the sum of their ages now?

A) 18
B) 24
C) 28
D) 35
E) 42

Thanks Mitch for the reply.
as you mentioned in case 2:

Case 2: Five years ago A=2 and E = 3*2 = 6
Sum of the their ages now = (2+5) + (6+5) = 18.
18 is not among the answer choices.

But 18 is among the answer choices as first answer choice is A)18

so how can we choose between A)18 and E)42?

Thanks

[GMATGuruNY]

Thanks Mitch for the reply.
as you mentioned in case 2:

Case 2: Five years ago A=2 and E = 3*2 = 6
Sum of the their ages now = (2+5) + (6+5) = 18.
18 is not among the answer choices.

But 18 is among the answer choices as first answer choice is A)18

Good catch.
I've edited my post accordingly.

so how can we choose between A)18 and E)42?

Thanks

In the edited post, I explain how to eliminate A.

[Brent@GMATPrepNow]

Below is a question by GMAT Prep Now.

5 years ago, Ebo was 3 times as old as Atu. In 3 years Ebo will be twice as old as Atu. What is the sum of their ages now?

A) 18
B) 24
C) 28
D) 35
E) 42

Here's the video solution that Pazoki noted: https://www.gmatprepnow.com/module/gmat ... /video/909

Cheers,
Brent

[Matt@VeritasPrep]

I got Aut as he/she is younger. So Ebo in 5 yaers ago is 3(A-5) and when we add 8 years to it we will get 3 years from now which will be 3(A-5)+8=2(A+3) ==> 3A-7=2(A+3),solved for "A" and got A=13, then plug "A" in in the equation to solve for Ebo or E=29 then E+A=> 29+13=42 (E) is correct.
Did I do correctly?

This is great! Be careful on test day, though: it's easy to lose track of what you're doing by trying to cut out the other variable. It might be safer just to say

3*(A - 5) = (E - 5)

and

2*(A + 3) = (E + 3)

From there, manipulate each equation so they each equal the same thing (E):

3*(A - 5) + 5 = E
2*(A + 3) - 3 = E

Then set the two left sides equal

3 * (A - 5) + 5 = 2 * (A + 3) - 3

to find Atu's age, from which it's easy to also find Ebo's age.