Lesson: Solving Age Questions

Comment on Solving Age Questions

It is accurate, yet a very simple technique.

I used one variable, starting with the smallest value. I assigned i = Iris 11 years ago, and 11 years ago Abbie was 3i. For the present, Iris was i + 11, and Abbie was 3i + 11. I then wrote the equation 4i + 22 = 42, and solved for i.

Then I solved for 3i + 11 + 2, which gave me 28.

Would this approach translate into other problems, using one variable but starting with the simplest set of variables, even if it's starting in the past?
greenlight-admin's picture

You're referring to the question that starts at 3:05 in the video.

Yes, that strategy also works. As long as your variable expressions match the given information, your approach will work.

You'll see that we used 1 variable to solve the first questions and 2 variables to solve the second question. I let students decide what works best for them. The 2-variable approach requires us to solve a system of equations, and the 1-variable approach can result in equations/expression that are more complex, but both approaches will work.

hello, Can you add how to do question at 3:05 with one variable? ur way not asedien. thank you for ur help like always.
greenlight-admin's picture

Glad to help!

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

This means that....
x-11 = Abbie's age 11 YEARS AGO
42-x-11 = Iris' age 11 YEARS AGO
Simplify to get: 31-x = Iris' age 11 YEARS AGO

Given: 11 years ago, Abbie was 3 TIMES as old as Iris
We can write: Abbie's age 11 years ago = 3(Iris' age 11 years ago)

So we get: x-11 = 3(31-x)
Expand: x - 11 = 93 - 3x
Add 3x to both sides: 4x - 11 = 93
Add 11 to both sides: 4x = 104
Solve: 4 = 26

So, Abbie's PRESENT age = 26
So, Abbie will be 28 years old IN TWO YEARS

thx Brent for ur quick answer like always. I really recommend this website to anyone wants to learn math not only GRE math. Brent's explanations are wonderful and straight to the point, not mention that he answers ur questions very quickly & efficiency. I tried many websites , but this one was the best!
thank you Brent for everything.... u really into math and u likes it, and that gives u this gift to explain it v easily.
greenlight-admin's picture

Thanks AFNAN!

Hi Brent,

I solved this by testing answer choice
For 1st Question type

I took Soo present age = 12(Option C)
Hence marco age = 4(since Soo is 8yrs older)

Then in 4 yrs Soo age = 16 & Macro = 8(Now Soo age will be twice of macro from the question is satisfied) hence option C is correct.

For 2nd Question

I again took option C for Abbies age = 18(2 yrs from now) Current age of Abbies = 16
Hence Iris presnt age = 26 (sum of age is 42)
but we need abbies to be greater than Iris(condition from question)
Hence option C is incorrect also Option A&B cancel out.

Now I took option E i.e = 28
using the same approach

Abbie present age = 26
Iris age = 16 ( sum of age = 42)
after 11 yrs abbie age wil be = 15 & Iris age = 5
i.e abbie age is 3 time as old as Iris ( 5*3 = 15)

Hence option E correct answer.

Is this approach correct & will It work for all similar age questions.

I just tried bcz u said in 1st video of this section that testing option should be 1st approach.

Pls help.





greenlight-admin's picture

Your solutions are perfect.

As I mentioned in an earlier lesson, plugging in the answer choices is often a great approach. The main problem with that approach, however, is that it can be quite time-consuming for some questions. So, if you can identify an approach that may be faster, you should also consider that.

I should also mention that there are times when we can't plug in the answer choices. For example, if the question asks us to find the SUM of Joe's and Mel's ages, then we can't really do much with the answer choices.

Cheers,
Brent

https://gre.myprepclub.com/forum/meg-is-twice-as-old-as-rolf-but-three-years-ago-she-was-tw-11392.html

I would like to know why are we not subtracting 3 years from Rolf's current age as it is given in the question? Thanks Brent!
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/meg-is-twice-as-old-as-rolf-but-three-y...

We don't subtract 3 from Rolf's age, because we're told that "three years ago, she was two years older than Rolf is NOW"

Does that help?

Cheers,
Brent

https://gre.myprepclub.com/forum/re-qotd-2-if-1-2-x-years-ago-adam-was-12-and-1-2-x-3407.html

Hi Brent!

It's getting little difficult for me to understand this aforementioned question. Could you please help me out?

Thanks,
Ketan
greenlight-admin's picture

Hi Ketan,

Here's my full solution: https://gre.myprepclub.com/forum/re-qotd-2-if-1-2-x-years-ago-adam-was-1...

Cheers,
Brent

Solving from the 4minute mark. How come, to get the second equation, we could not simply subtract 11 years x2 from 42 and multiple 3 by A to get: 3A + I = 22 as the second equation? We would then subtract the two equations (A+I=42 - 3A+I=22) from one another. How come this doesn't work? What connection am I assuming or missing with this logic?
greenlight-admin's picture

I'm not sure what "x2" is referring to in your post.
Do you mean to subtract 11 twice from 42?
If so, that would be 20 (not 22..thus my confusion)

Also, we're told that Abbie was 3 times as old as Iris.
So, if Abbie is already 3 times as old as Iris, we cannot make their ages equal by multiplying A (Abbie's age) by 3.

If I'm 3 times as old as you are. We must multiply your age (the younger person) by 3 in order to create an equation.

Does that help?

Cheers,
Brent

Hi Brent,
I'm having difficulty interpreting the age value, specially in cases when to add or multiply the centered information and how to apply it to each individual.

Like for instance, if someone is "as much as old" as someone else, or if x is n older than y. Hopefully I'm making sense.

what would be a good strategy to be able to overcome this issue.
Thanks
greenlight-admin's picture

Let's start with some fundamentals.

1) If Joe is n years OLDER THAN Sue, then we can write:
(Joe's age) = (Sue's age) + n

2) If Joe is k TIMES AS OLD AS Sue, then we can write:
(Joe's age) = k(Sue's age)

Does that help?

To reinforce these concepts, Keep answering questions from the Reinforcement Activities box.

Yes it is actually helpful.
So whatever comes after "is" is applied to the 2nd person " in a sense" to make the 2 quantities equal. Is this an accurate conclusion?
greenlight-admin's picture

I'm not 100% sure what you're asking, but I can tell you that IS typically represents "="

Take for example: Joe is n years OLDER THAN Sue
We can first say: Joe's age = n years OLDER THAN Sue
And then say: Joe's age = Sue + n
-----------------------
Another example: Joe is k TIMES AS OLD AS Sue
We can first say: Joe's age = k TIMES Sue's age
And then say: (Joe's age) = k(Sue's age)

Cheers,
Brent

Very hard question from one of the linked questions. Comes from Barron's GRE (so I'm already suspicious):

If x/2 years ago Adam was 12, and x/2 years from now, he will be 2x years old, how old will he be 3x years from now?

A 54
B 18
C 24
D 30
E It cannot be determined from the given information.

This is ranked medium? No way! Put it HARD. If only half the people got this question right, it needs to be HARD difficulty. Extremely difficult to understand!
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/re-qotd-2-if-1-2-x-years-ago-adam-was-1...

Keep in mind that, on this site, "medium" is classified as 150-159 (aside: in quant as 159 is a 73rd percentile score).

At the moment, the question has been answered only 8 times, so the sample size may not be large enough to confirm this question is in the 160+ bracket.
I think the level of difficulty is in the high 150's. However, it could very well be in the low 160's.
So, I've changed it to 160-170

Cheers,
Brent

Hey Brent,

Why do you, at 5:20, when presenting the systems of equations flush with each other, multiply the original equation (A+I)=42 by 3?
greenlight-admin's picture

Great question!

Let's start with our system:
A + I = 42
A - 3I = -22

When using the elimination method with systems of equations, our goal is to eliminate one of the variables.
Since we have 1A in both equations, I COULD have just subtracted for the bottom equation from the top equation to get: 4I = 64
Solve to get I = 16
However, since the question is asking for the value of A, we still need to plug I = 16 into A + I = 42 in order to find the value of A.

To avoid that last step, I decided to eliminate the terms with variable I (which who would leave me with the variable we're asked to find: A).
To do this, I multiplied both sides of the pop equation by 3 to get:
3A + 3I = 126
A - 3I = -22

Now that we have 3I in both equations, we can ADD the equations to get: 4A = 104
Solve to get: A = 26

As you can see, both methods reach the same conclusion (A = 26).

Both approaches probably take about the same time. I prefer my approach ONLY because it helps me avoid the trap of selecting the wrong answer choice.
If I were to use the first approach and determine that I = 16, I might accidentally conclude that the correct answer is 16 and choose answer choice A.
Isolating the target variable (A in this case) helps me avoid this potential mistake.

Cheers,
Brent

How does one decide whether it is best to use to equations, such as "let A=Abbie's age and let I= Iris's age," rather than the method used in the first question?

Additionally, how are you able to multiply the top equation in the systems of equations by 3 (A + I=42 becomes 3A+3I=126) after the 5 minute mark?
greenlight-admin's picture

Good questions. Here are my responses:

1) For many word problems, we have the option of assigning one variable or more than one variable. If you assign just 1 variable, the resulting equation will be more complex than the equations you'll create if you assign more than one variable. However, when you assign more than one variable, you end up with a system of equations that can sometimes take longer to solve.

In the video solution above, we used two variables (A and I) to solve the question about Abbie and Iris.
We could have also used just one variable.
For example, we could let A = Abbie's PRESENT age
In that case, 42 - A = Iris' PRESENT age (since their ages add to 42)

So A - 11 = Abbie's age 11 YEARS AGO
And 42 - A - 11 = Iris' age 11 YEARS AGO
....etc.

Our solution is still the same.

For more on how many variables to assign, watch this video: https://www.greenlighttestprep.com/module/gre-word-problems/video/907

2) As long as we perform the same operation to BOTH sides of an equation, the resulting equation will be equivalent to the original equation.
Take, for example, the equation: 2x + 1 = 7 (solution: x = 3)
Add 5 to both sides of the equation to get: 2x + 6 = 12 (solution: x = 3)
Multiply both sides of the original equation by 4 to get: 8x + 4 = 28 (solution: x = 3)
Subtract 11 from both sides of the original equation to get: 2x - 10 = -4 (solution: x = 3)

For more on solving systems of questions, you can watch: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

How do you know when to subtract or add the different equations?
greenlight-admin's picture

If we have a system of two equations with two variables, we can quickly eliminate one variable (so we can focus on the other variable) if both equations have a coefficient in common.

For example, the equations 2x + 3y = 8 and 2x + y = 4 both have the term 2x.
So if we SUBTRACT the second equation from the first equation, the x terms disappear to get: 2y = 4

Similarly, the equations 2x + 5y = 12 and 4x - 5y = -6 have the term 5y and -5y.
So if we ADD the two equations, the y terms disappear to get: 6x = 6

For more on this strategy, watch the following video (starting at 3:10): https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Why at the 5:03 mark did you multiply by 3? I do not understand :-(
greenlight-admin's picture

Good question!!

We have the following system of equations:
A + I = 42
A - 3I = -22

Notice that we have two options:
i) Eliminate the A's and first solve for I.
ii) Eliminate the I's and first solve for A.

Keep in mind that our goal is to solve the system for A.
If we go with option i, then we still have an extra step after solving for I.
That is, once we have the value of I, we must plug it into one of the given equations so that we can solve for A.

On the other hand, if we go with option ii, then we don't have that extra step.
For this reason, I multiplied both sides of the top equation by 3 to get:
3A + 3I = 126
A - 3I = -22
Then I added both equations to get: 4A = 104, which means A = 26

Having said that, I could have also gone with option i.
Let's do that now...

Take:
A + I = 42
A - 3I = -22

Subtract the bottom equation from the top equation to get: 4I = 64, which means I = 16
Now plug I = 16 into the first equation (A + I = 42) to get A + 16 = 42, which means A = 26

So, as you can see, both options work.

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