# Question: Value of x+2y

## Comment on Value of x+2y

### Can you please explain how

Can you please explain how you factored x^2+4xy-5y^2=15?

### We're going to factor the

We're going to factor the left side of x² + 4xy - 5y² = 15

That is, we want to factor x² + 4xy - 5y²
For many students the y's complicate matters, so let's just IGNORE the y's for the time being and try to factor x² + 4x - 5

Well, we know that x² + 4x - 5 = (x + 5)(x - 1)
Okay, now let's put the y's back and see how we do.
x² + 4xy - 5y² = ?

Well, since x² + 4x - 5 = (x + 5)(x - 1), we can see that x² + 4xy - 5y² = (x + 5y)(x - 1y)

If we want to test whether this is true, just take (x + 5y)(x - 1y) and EXPAND it by applying the FOIL technique (https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...)

When we do this, we see that...
(x + 5y)(x - 1y) = x² - 1xy + 5xy - 5y²
= x² + 4xy - 5y²
Perfect!!

So, going back to the original equation, we get:
x² + 4xy - 5y² = 15
(x + 5y)(x - 1y) = 15

### Why cant we do like:

Why cant we do like:

Plug in the value of y (y = x-3) in the given equation (x^2 - 5y^2 + 4xy - 15 = 0) and then find the value of x (which comes out to be 2.4) and the plug it back in (y = x-3), then we get y = -0.6

And then we can find 'x+2y' which come out to be 1.2 ?

### That approach is totally

That approach is totally valid. However, it does require a bit of work as well.
I should also note, that when we do this and solve for x, we get x = 10/3 (not x = 2.4)

If we replace y with x-3, we get: x² - 5(x-3)² + 4x(x-3) - 15 = 0
Expand: x² - 5(x² - 6x + 9) + 4x(x-3) - 15 = 0
Expand again: x² - 5x² + 30x - 45 + 4x² - 12x - 15 = 0
Simplify: 18x - 60 = 0
Solve: x = 10/3

Take x = 10/3, and plug this value into the equation y = x-3, to get: y = 10/3 - 3 = 1/3

So, x = 10/3 and y = 1/3, which means x + 2y = 10/3 + 2(1/3) = 10/3 + 2/3 = 12/3 = 4

### Thank you so much !..

Thank you so much !..
I did a silly mistake while finding the value of 'x'. My Bad !

### I did this substitution

I did this substitution method and got the result pretty quickly. But thank you for explaining the factoring trick in the previous comment. Really helpful; otherwise I prefer substituting to factoring when x,y are present in an equation together. Your trick helps simplify that approach. I will practice that for future! :)

Beautiful!

### hi,

hi,

I worked on the second equation and ended up with (x + 5y)(x - y)=15

x + 5y = 15 (substitute initial info y = x - 3)
x + 5 (x-3) = 15
x + 5x - 15 = 15
x = 5

x - y = 15 (substitute initial info y = x - 3)
x - x + 3 = 15
3 = 15 (therefore, theres no need to continue with x-y = 15 as a solution)

using the first solution (x=5)
y=x-3
y=5-3
y=2

therefore, x + 2y = 5 + 2(2) = 9

this is the wrong answer. Can you help me understand:

- is this a valid approach
- if so, where am I going wrong

Thanks so much

### You are correct to say that

You are correct to say that (x + 5y)(x - y) = 15

However, you then conclude that EITHER x + 5y = 15 OR x - y = 15. This part is incorrect.

You are taking a different rule and making a new rule that doesn't apply.

Here's what I mean:

If AB = 0, then we can conclude that EITHER A = 0 OR B = 0. NOTE: this only works because our product is ZERO.

However, if AB = 15, we cannot conclude that EITHER A = 15 or B = 15. For example, it could be the case that A = 3 and B = 5. Or it could be the case that A = 2 and B = 7.5, etc.

Does that help?

Cheers,
Brent

### You are correct to say that

You are correct to say that (x + 5y)(x - y) = 15

However, you then conclude that EITHER x + 5y = 15 OR x - y = 15. This part is incorrect.

You are taking a different rule and making a new rule that doesn't apply.

Here's what I mean:

If AB = 0, then we can conclude that EITHER A = 0 OR B = 0. NOTE: this only works because our product is ZERO.

However, if AB = 15, we cannot conclude that EITHER A = 15 or B = 15. For example, it could be the case that A = 3 and B = 5. Or it could be the case that A = 2 and B = 7.5, etc.

Does that help?

Cheers,
Brent

### Brent, how are you?

Brent, how are you?

https://gmatclub.com/forum/what-is-the-value-of-x-yz-167499.html

I mean, as per the question stem, we are trying to find x/zy, which is the same as x/z * x/y.

Now let's move onto statement 1: It tells me exactly what I need, since x/y = 1/2 and x/z = 5/2

On the statement 2 the information provided will not be sufficient, since there will be a lack of information regarding the value of z.

Can you help me out? Please.

Regards,

Pedro Tucci

Hi Pedro,
I'm doing well, thanks!

You made a small error at the beginning of your solution, and this error causes the issue.

You wrote: "I mean, as per the question stem we are trying to find x/zy, which is the same as x/z * x/y"

Be careful, x/zy does NOT equal x/z * x/y, since x/z * x/y = x²/zy (not x/zy)

Does that help?

Cheers,
Brent

### Hi Brent, I'm doing fine as

Hi Brent, I'm doing fine as well.

It totally helps, I have not noticed this silly mistake.

My prep is great, now I'm reviewing all the valuable material you built and training as hard as possible my test taker abilities so that I can excel in the GMAT next month.

I'd like to use this opportunity to congratulate you for the quality of the material you put together here, it is really good and easy to understand, a really walking through by the concepts of the GMAT. I'm glad to have find you on may way, it will made a total difference in my future. Thank you so much. Anything you want you can count on me (provided that I'm from Brazil....heheheh).

Best,

Pedro

### Hi Pedro,

Hi Pedro,

Thanks for the kind words about the course! I'm glad you like it.
All the best on your test!!!

Cheers,
Brent

### Hi Brent,

Hi Brent,

Do you have any other books or resources you'd recommend that might help me with number sense? I know that's a general question and the answer is probably just to keep drilling and trying to find alternative ways of solving problems, but if you have any other tips I'd appreciate it!

It simply never would've occurred to me to set the factorization equal to 15 (rather than 0) and then recognize that x-y = 3 to complete the equation.

### I should first tell you that

I should first tell you that this is a SUPER hard question. So, you shouldn't be too discouraged if you didn't answer it correctly.

You predicted my response perfectly. I will add that you should also spend a lot of time reviewing the responses from the Experts (including mine :-) on the GMAT forums. You will often discover some novel/clever properties/strategies involving number sense.

Cheers,
Brent

### Hey Brent,

Hey Brent,

https://gmatclub.com/forum/if-ksn-is-defined-to-be-the-product-of-n-k-n-k-1-for-all-posi-305859.html

I can´t follow up, I don´t even really understand the question and what S is suposed to be?

Philipp

### This is known as a Strange

This is known as a Strange Operator question. More on this question type here: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Here's my full solution: https://gmatclub.com/forum/if-ksn-is-defined-to-be-the-product-of-n-k-n-...

Cheers,
Brent