Question: Ages of Ebo and Atu

Comment on Ages of Ebo and Atu

Hi Brent,
How could it be solved by assigning 1 variable? I could solve by test the answer though takes a lot of time but don't know how to approach by using 1 variable.
Thank you
gmat-admin's picture

Using 1 variable is a little trickier.
One approach is as follows:
Let A = Atu's age FIVE YEARS AGO
So 3A = Ebo's age FIVE YEARS AGO
Now let's determine their ages 3 years in the FUTURE (which is 8 years away from 5 years ago)
A + 8 = Atu's age IN THREE YEARS
3A + 8 = Ebo's age IN THREE YEARS
We're told that, in 3 years, Ebo is TWICE as old as Atu.
So, to make their futures ages EQUAL, we must double Atu's age. We get:
2(A + 8) = 3A + 8
Solve to get: A = 8
Since A represents Atu's age FIVE YEARS AGO, then Atu's PRESENT age is 13
Likewise, we see that 3A represents Ebo's age FIVE YEARS AGO. So, age FIVE YEARS AGE was 3(8), which equals 24.
So, Ebo's PRESENT age is 29
So, the sum of their PRESENT ages = 13 + 29 = 42

Hi, I did it using single variable as you have shown above.
However, I am still not clear what are the best way to solve the word problems:
1.) either using single variable or by using double variable ?
2.) Assuming current age as A+5 (and take 5 yrs ago as A) OR assuming present age as 'A' and 'A-5' five year ago.
Pls advice in which chase the equation will be simpler.

gmat-admin's picture

Good question. I cover those questions in the following videos:

How Many Variables to Assign:

Solving GMAT Age Questions:

Hi Brent,
I tried solving this way: Can you tell me what am I missing?

Atu age´s 5 years ago: A-5
Ebo age´s 5 years ago:3(A-5)
Why it doesnt´work?
gmat-admin's picture

Your equation A-5 = 3A-15 suggests that Atu age´s 5 years ago = 3 TIMES Atu age´s 5 years ago. This cannot be true.

It's like saying, the money in my bank account = 3 TIMES the money in my bank account.

To solve this question, you need to use the second piece of information (In 3 years, Ebo will be twice as old as Atu)

Hi Brent,

Can you please solve PS01648 from OG 2019 edition (Q 225)?

gmat-admin's picture

Hi Kashaf,

In the future, please include the first sentence or two of the question so I can easily search for that question.

Here's my full solution:


Hi Brent,
In Q304 of OG 2019 (DS05330), isn't statement 1 sufficient? It says that p>q, but if P is 418 (>q) units then total profit is less than 2000. Similarly if p=834 then also profit is less than 2000. This means that as long as p>q, profit is less than 2000. Isn't this sufficient?

gmat-admin's picture

Here's the question:

A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.

From the given information we know that:
For each unit of P sold, the PROFIT = $2.00 ($10 - $8 = $2)
For each unit of Q sold, the PROFIT = $3.50 ($13 - $9.50 = $3.50)

Case I: The company sold 418 units of product P, and sold 416 units of product Q
TOTAL PROFIT = (418)($2) + (416)($3.50) = $836 + $1456 = $2292
So the answer to the target question in this case is "YES, the profit was more than $2,000"

Case II: The company sold 834 units of product P, and sold 0 units of product Q
TOTAL PROFIT = (834)($2) = $1668
So the answer to the target question in this case is "NO, the profit was no more than $2,000"

So, statement 1 is not sufficient

Does that help?

Hi Brent,

Thanks for providing such great material to study!

Is there a quicker solution to solving such word problems?

gmat-admin's picture

The strategy of using a table to organize your thoughts shouldn't take up a lot of extra time.
That said, you can always try solving age question without a table and see if that saves you any time.


Hi Brent, can you give me a hand with this one plase Rachel’s mother is 21 years older than her. The ratio of their current ages is 2:1. What will be the corresponding
ratio of their ages 9 years from now? the answer is 17:10
gmat-admin's picture

Hey Miguel,

When posting questions, please post all five answer choices as well.
In many cases, the fastest approach to solving a GMAT question involves testing the answer choices.


gmat-admin's picture

Let R = Rachel's PRESENT age
Let M = Her mom's PRESENT age
From the first piece of information we can write: M = R + 21 (since the mother is 21 years older than Rachel)

From the second piece of information, we can write: M/R = 2/1 (since the ratio of their current ages is 2:1)
Cross multiply to get: M = 2R

We now have a system of equations:
M = R + 21
M = 2R

Since both equations are set equal to M, we can write: 2R = R + 21
Solve: R = 21

This means Rachel's PRESENT age is 21, which means her mom's PRESENT age 42 (since she is 21 years older than Rachel)

If Rachel's present age is 21, her age IN 9 YEARS will be 30
If her mom's present age is 42, her age IN 9 YEARS will be 51

So the ratio of their ages IN 9 YEARS will be 51 : 30
To simplify this ratio, we can divide both parts by 3 to get 17 : 10


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