Lesson: Solving GMAT Age Questions

Comment on Solving GMAT Age Questions

Assuming the question changes to 4 years ago, Soo was twice as old as Marco. Will the equation change to 1/2(M+4)?

I was working on this question here (http://www.beatthegmat.com/equations-t269315.html#691952) and the age translation changed. Does the past and future change whether equation translation?
gmat-admin's picture

If the question were worded so that it gave information about their ages 4 years AGO, then...
4 years ago, Marco's age was M-4
And 4 years ago, Soo's age was M+4
Since Soo was twice as old as Marco, we need to DOUBLE Marco's age to make the ages equal.
So, M+4 = 2(M-4)

I dont understand why you are doubling marcos age?
gmat-admin's picture

We're told that Soo is twice as old as Marco.

Our goal is to create an EQUATION. However, at the moment, we cannot say that their ages are equal since Soo's age is much bigger than Marco's age.

So, how can we make their ages equal?

We can take the smaller age (Marco's age) and double it so that it equals Soo's age.

More here: https://www.gmatprepnow.com/module/gmat-word-problems/video/903

So, I go:
Marco = M
Soo = M+8
In 4 years,
Soo = (M+8)+4
Marco = M+4
Given:
M+8+4 = 2(M+4)
M=4
Soo's age = 4+8 = 12
gmat-admin's picture

Perfect!

Hey Brent,
Just a question: Is this question really a possible question we could see on the GMAT considering how long it generally takes to solve it? Or is it just to reinforce concepts.
"In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice?"

Also I found a decent way to solve to question really fast.

Since we know that the answer choices are all Janice's age, and that Janice's age 6 years ago was a perfect square. I subtracted 6 from all answer and only one of them yielded a perfect square (42 -6 = 36).
In the event another answer also yielded a perfect square, we can test her daughters age 6 (root of 36) by adding 9 (6 years ago + 3 years hence) = 6 + 9 = 15.
Also Janice's age 42 + 6 = 45. This satisfies the condition of Janice's age 3 years hence being thrice the daughters age. Verifying the fact that we have the correct answer.

Thanks !
gmat-admin's picture

Here's the link to your question: https://gmatclub.com/forum/in-three-years-janice-will-be-three-times-as-...

I think all of the linked questions in the Reinforcement Activities box are representative of the GMAT.

Your solution is PERFECT!! In fact, I have posted it here (with kudos to you, of course!): https://gmatclub.com/forum/in-three-years-janice-will-be-three-times-as-...

Hi Brent

In the single variable explanation of the Abbie Iris question. Can you always assume the smallest number number = the variable. The reason I ask this is that it seems that you miss a step if you go from Iris age=I and therefore Abbie's age = 42-I. Why would you not write Iris's age in terms of the sum of 42 as well?

That is where I got bogged down. I tried to use the sum as my reference, therefore Abbie Age + Iris Age = 42, therefore Iris Age = 42 - Abbie age and Abbie age = 42 - Iris's age.

This did led me down the wrong path. Any tips?

Kind regards
gmat-admin's picture

Great question, Willem!

I find it easier to assign the single variable to the smaller age. That way, we can often avoid using fractions and negatives.

That said, we could have just as easily assigned the variable to Abbie's PRESENT age. Let's do that.

Let A = Abbie's PRESENT age
So, 42 - A = Iris's PRESENT age

11 years ago, each person was 11 years YOUNGER. So...
A - 11 = Abbie's age 11 YEARS AGO
So, 42 - A - 11 = Iris's age 11 YEARS AGO

Simplify to get:
A - 11 = Abbie's age 11 YEARS AGO
So, 31 - A = Iris's age 11 YEARS AGO

GIVEN: 11 years ago, Abbie was three times as old as Iris.

In other words:
(Abbie's age 11 YEARS AGO) = 3(Iris's age 11 YEARS AGO)
We get: A - 11 = 3(31 - A)
Expand: A - 11 = 93 - 3A
Add 3A to both sides: 4A - 11 = 93
Add 11 to both sides: 4A = 104
Solve: A = 26

So, Abbie's PRESENT AGE is 26

The question asks for Abbie's age in 2 years.
Answer = 26 + 2 = 28

Does that help?

Cheers,
Brent

Hi, are age questions a major part in GMAT test?
gmat-admin's picture

No, age questions aren't a huge part of the GMAT. However, many of the skills needed to answer age questions are transferable to other question types.

Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum of their ages will be 51, how old is Stephanie ?

A. 6
B. 10
C. 14
D. 20
E. 24

Present:

Kate= K
Stephanie= 3K-4
Jim= 2*(3K)-4

In 5 years:

Kate= K+5
Stephanie= 3K-4+5
Jim= 2*(3K)-4+5

I'm trying to solve this equation with only one variable (smallest value), but I think I have assigned the variables wrong since the equation doesn't turn out to be correct. Can you please advise on my mistake.
gmat-admin's picture

The main problem is with Stephanie's PRESENT age (which you say is 3K-4)

If K = Kate's PRESENT age, then K - 4 = Kate's age 4 YEARS AGO
So, 3(K - 4) = Stephanie's age 4 YEARS AGO
Which means 3(K - 4) + 4 = Stephanie's PRESENT age
Simplify to get: 3K - 8 = Stephanie's PRESENT age

This also means 2(3K - 8) = Jim's PRESENT age

Here's my full solution to the question: https://gmatclub.com/forum/jim-is-twice-as-old-as-stephanie-who-four-yea...

Cheers,
Brent

By present age I meant Age 4 years ago. I saw some mistakes I did and corrected them below:

Age 4 years ago:

Kate= K
Stephanie= 3K-12
Jim= 2*(3K-12)

In 5 years: (+9 since -4 years+ 5 years in the future)

Kate= K+9
Stephanie= 3K-12+9
Jim= 2*(3K-12)+9

K+9+3K-12+9+6K-24+9=51
10K-9=51
10K=51+9
10K=60/10
K=6

3*6-12=6 (Stephanie's age 4 years ago)
6+4=10 (Stephanie's present age)

I think it can be solved like this as well. I want to learn to solve everything with only one variable since I personally find it easier. This seemed like a hard question to me. What score would you say this question is worth?
gmat-admin's picture

I'd say it's in the 600-650 range.

Cheers,
Brent

For this question, I did testing answer choices, beginning with 12 years as Soo's age. Thankfully, it worked out: If Soo is 12; Marco is 4 (since Soo is 8 years older; In 4 years, Soo will be 16 and Marco will be 8, which satisfies that Soo's age will be twice that of Marco's.

In this case, testing answer choices gets to the correct answer faster - right? Thanks!
gmat-admin's picture

If you tested answer choice C first, then testing values was most likely the fastest approach for you.
Of course, that also depends on how quickly you can solve the question algebraically.

Throughout this course I am trying to do all the exercises of the videos ...
In this exercise I got a wrong result: Abbie will be 28 in the future:

(Present)
A + I = 42

then...

(Past)
A + I = 20 (because -11 - 11)

Therefore ... (in the past)

A = 3I
I = A / 3 and A = 20 - I

then (substitute I)...
A = 20 - A / 3
A = (60-A) / 3
A = 15. Abbie was 15 years old in the past.

11 years later (present) she is 15 + 11 = 26

and in two years (in the future) she will be 26 + 2 = 28

Abbie will be 28 in the future.

What am I doing wrong?
gmat-admin's picture

In your solution, you're saying that:
A = Abbie's PRESENT age
I = Iris's PRESENT age

So, in your equation A = 3I, you're saying that Abbie's PRESENT age is 3 times Iris's PRESENT age.
However, the question tells us that Abbie's age ELEVEN YEARS AGO was 3 times Iris's age ELEVEN YEARS AGO.

If A = Abbie's PRESENT age, then A-11 = Abbie's age ELEVEN YEARS AGO
If I = Iris's PRESENT age, then I-11 = Iris's age ELEVEN YEARS AGO

So we should write: A-11 = 3(I-11)

Does that help?

https://gmatclub.com/forum/five-years-ago-jim-was-three-times-as-old-as-raoul-was-and-monica-was-237208.html

Hey Brent, for this question, why aren't we subtracting 5 from everyone's age vs just Raouls?
Ex. My equation for Jim was J-5=3(R-5)
gmat-admin's picture

Question link: https://gmatclub.com/forum/five-years-ago-jim-was-three-times-as-old-as-...

There is an important distinction between your solution and my solution. My solution involves only 1 variable, while your solution involves 2 or more variables.

So, in my solution I let R = Raoul's PRESENT age, which means R - 5 = Raoul's age 5 YEARS AGO.
The question tells us that "Five years ago, Monica was six years older than Raoul was."
If R - 5 was Raoul's age 5 YEARS AGO, then that means (R - 5) + 6 was Monica's age 5 YEARS AGO.
In other words R + 1 was Monica's age 5 YEARS AGO.
etc

However if we decide to say R = Raoul's PRESENT age and J = Jim's PRESENT age, then...
R - 5 was Raoul's age 5 YEARS AGO and J - 5 was Jim's age 5 YEARS AGO, in which case your equation J - 5 = 3(R - 5) is perfect.

So, just keep in mind that, a solution using 1 variable will look quite a bit different from a solution using more than 1 variable.

100% agree and follow. I asked because I got a different solution. But I'm also 100% positive my math was bad at some point. So ill go back and revise to see where. Thank you!

can I get the solution of this
https://gmatclub.com/forum/a-company-makes-and-sells-two-products-p-and-q-the-costs-per-unit-of-217551.html

Hi Brent,
For the 2nd part of this video (Abbie-Iris) I solved and got Abbie's age as 26 but I missed the part of the question that says "Abbie's age in 2 years." This is something that I struggle with. Maybe it's because I always use a timer when I'm trying to solve these questions. How do I ensure I always read the full question? Any strategies or tips aside from more practice?
Thanks in advance!
gmat-admin's picture

I cover a variety of ways to avoid silly mistakes in the following article: https://www.gmatprepnow.com/articles/avoiding-silly-misteaks-gmat

Having said that, I believe one of the best approaches is to:
1) Read the question
2) Solve the question
3) RE-read the question before entering your response

While solving the question, you gain a deep understanding of the key/crucial components of the question. So, when you later re-read the question, any information you missed during the first read will become more apparent.

While this approach will eat up sometime, I think it's the best way to catch potential reading errors.

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