The value of an investment increases by x%

[tim]

I hesitate to say that there is any "best" approach to this problem; different students will find different strategies useful. My advice though would be to make sure you know how to use an algebra approach AND a picking numbers approach effectively on this one. The more you can become familiar with multiple approaches to a given question type, the better prepared you will be for similar questions on the real test.

[rustom.hakimiyan]

I hesitate to say that there is any "best" approach to this problem; different students will find different strategies useful. My advice though would be to make sure you know how to use an algebra approach AND a picking numbers approach effectively on this one. The more you can become familiar with multiple approaches to a given question type, the better prepared you will be for similar questions on the real test.

Hi Tim,

Two questions on this:

1) I can follow the MGMAT explanation pretty well but when I started to solve this, I came up with two equations and two unknowns (which didn't yield the correct answer)

EQ 1: xy(Investment)=Investment
EQ 2: x(Investment) + y(Investment) = Investment

My answer was y = -x^2 which is obviously wrong. Can you please comment if this approach was incorrect? I don't normally think of adding/subtracting percentages as 1 + (rise/fall)/100, instead I usually just multiply it by 1, so a 10% increase is 1.1 rather than 1 + (10/100).

2) How would choosing numbers work in this scenario? I wouldn't even know how to pick a number that would work for the first step?

Thanks!

[RonPurewal]

1) I can follow the MGMAT explanation pretty well but when I started to solve this, I came up with two equations and two unknowns (which didn't yield the correct answer)

EQ 1: xy(Investment)=Investment
EQ 2: x(Investment) + y(Investment) = Investment

My answer was y = -x^2 which is obviously wrong. Can you please comment if this approach was incorrect? I don't normally think of adding/subtracting percentages as 1 + (rise/fall)/100, instead I usually just multiply it by 1, so a 10% increase is 1.1 rather than 1 + (10/100).

The 1.1 thing is right. But, if you're going to do that algebraically, you HAVE to use 1 ± (p/100), where p is the percent decrease or increase.
I.e., if you want to increase something by 10%, then you have to multiply by 1.10, which is 1 + 10/100.
You can't just convert 10% to a decimal (= 0.10) and multiply by it. That would give you 10% of the original number, which is clearly not what you want here.

For the same reason, if you want to increase something by p%, you can't just multiply by p or p/100%. You don't want to take p% of the number.

Just in case you don't know, here is where this expression comse from:
Original number increased by p%
= original + (p%)(original)
= original + (p/100)(original)
= (1 + p/100)(original)

Without the "1 +" part, it's just a percent OF a number, not a percent change.

[RonPurewal]

2) How would choosing numbers work in this scenario? I wouldn't even know how to pick a number that would work for the first step?

Thanks!

Well, you have to "undo" the percent change in the next step, so pick a percent change that is easy to "undo".

If I were doing this problem, I would take the original number and increase it by 100%. That way it becomes twice as big, so it's pretty easy to see that the next step is a 50% decrease. So, x = 100 and y = 50 will work.
If more than one choice works with these numbers, I'll just pick other ones.

[rustom.hakimiyan]

1) I can follow the MGMAT explanation pretty well but when I started to solve this, I came up with two equations and two unknowns (which didn't yield the correct answer)

EQ 1: xy(Investment)=Investment
EQ 2: x(Investment) + y(Investment) = Investment

My answer was y = -x^2 which is obviously wrong. Can you please comment if this approach was incorrect? I don't normally think of adding/subtracting percentages as 1 + (rise/fall)/100, instead I usually just multiply it by 1, so a 10% increase is 1.1 rather than 1 + (10/100).

The 1.1 thing is right. But, if you're going to do that algebraically, you HAVE to use 1 ± (p/100), where p is the percent decrease or increase.
I.e., if you want to increase something by 10%, then you have to multiply by 1.10, which is 1 + 10/100.
You can't just convert 10% to a decimal (= 0.10) and multiply by it. That would give you 10% of the original number, which is clearly not what you want here.

For the same reason, if you want to increase something by p%, you can't just multiply by p or p/100%. You don't want to take p% of the number.

Just in case you don't know, here is where this expression comse from:
Original number increased by p%
= original + (p%)(original)
= original + (p/100)(original)
= (1 + p/100)(original)

Without the "1 +" part, it's just a percent OF a number, not a percent change.

Hi Tim,

Thanks for the clarification. I understand what you're trying to say here so let me take it a step further and see if i'm doing this wrong?

10 % Percent increase = (1 + (10/100)) Original Investment
Percent increase = (1.1)Original Investment

Am I right in assuming that both of the above equations are correct?

So if I tried to solve the equation using the latter of the two -- I would get something along the lines of: Investment(1.x)(.y) = I, solving this ends up being quite messy as I end up with .y = 1/1.x -- I don't really know whether I should multiply by 10 or 100 because I don't know the quantity it has increased by. Am I correct with the above analysis?

Thanks!

[RonPurewal]

I'm not Tim.

10 % Percent increase = (1 + (10/100)) Original Investment
Percent increase = (1.1)Original Investment

^^ These are correct.

So if I tried to solve the equation using the latter of the two -- I would get something along the lines of: Investment(1.x)(.y) = I, solving this ends up being quite messy as I end up with .y = 1/1.x -- I don't really know whether I should multiply by 10 or 100 because I don't know the quantity it has increased by. Am I correct with the above analysis?

"1.x" and "0.y" are not things that exist. You can't insert a variable into an expression as though it were a digit(s).

The non-existence of such things is, in fact, the entire reason why you have to use relatively clunky expressions like 1 ± thing/100.

[RonPurewal]

By the way"”If you get lost in the algebra, you should quit immediately, and start picking numbers.

[rustom.hakimiyan]

I'm not Tim.

10 % Percent increase = (1 + (10/100)) Original Investment
Percent increase = (1.1)Original Investment

^^ These are correct.

So if I tried to solve the equation using the latter of the two -- I would get something along the lines of: Investment(1.x)(.y) = I, solving this ends up being quite messy as I end up with .y = 1/1.x -- I don't really know whether I should multiply by 10 or 100 because I don't know the quantity it has increased by. Am I correct with the above analysis?

"1.x" and "0.y" are not things that exist. You can't insert a variable into an expression as though it were a digit(s).

The non-existence of such things is, in fact, the entire reason why you have to use relatively clunky expressions like 1 ± thing/100.

Ahhhhh -- got it. Learning something new everyday. Thanks!

[RonPurewal]

Sure.