Mistake in GMAT DS videos?!

[minihobel]

Hi!

I'm going straight to the point:

on: https://www.gmatprepnow.com/module/gmat-data-sufficiency ; Video 14. "Choosing a statement" on minute 4:48 there's the following stated:

What is the value of 5x^2 + 1?
(1) x^3 - x^2 - 9x + 9 = 0
(2) 2x + 5 = 11

-> (2) is sufficient (no comments on that one)!

My problem of understanding lies with the presented method to solve eq. (1)

In the video it is solved as follows:

1. x^3 - x^2 - 9x + 9 = 0
2. x^2(x-1) - 9(x-1) = 0
3. (x^2 - 9) (x-1) = 0
3. (x-3)(x+3)(x-1)= 0
Solution: x can be -3, 3, 1 => (1) is NOT sufficient

I dont understand!

Please have a look at no. 2. above...I'll solve differently
2. x^2(x-1) - 9(x-1) = 0
3. x^2(x-1) = 9(x-1)
4. x^2 = 9
Solution x = 3 or -3 (doesn't matter to answer the question) => (1) IS sufficient



I mean... did I something wrong or did they simply pick a confused example to prove poor statement choosing?!

Thanks [/u]

[Ian Stewart]

Let's first look at a simpler equation more likely to resemble what you'd see on the GMAT:

ab = a

You cannot just divide by a on both sides here and conclude that b=1, because it might be true that a=0, and you can never divide by 0. If you want to solve this equation by dividing by a, you must divide the problem into two cases:

1. either a=0 (quickly check if that could be true, and it can)

or

2. a is not 0, and we can divide by a on both sides, so b=1

So the equation ab=a means one of two things must be true: a=0, or b=1 (or they could both be true).

I'd never solve an equation like ab=a in that way, however. It's less confusing just to get 0 on one side and factor:

ab = a
ab - a = 0
a(b-1) = 0

so a=0 or b=1 (or both).

In your solution:

Please have a look at no. 2. above...I'll solve differently
2. x^2(x-1) - 9(x-1) = 0
3. x^2(x-1) = 9(x-1)
4. x^2 = 9
Solution x = 3 or -3 (doesn't matter to answer the question) => (1) IS sufficient

going from step 3 to step 4, you divided on both sides by x-1. You can't do that, because x-1 might equal 0. So you lost one of the solutions for x in that step. You don't run the risk of losing solutions in that way if you always factor equations like this.

[minihobel]

ah ok... Now I get it.
Thanks man

[Brent@GMATPrepNow]

you might be interested in this article called "Can You Divide by Variables?" https://www.gmatprepnow.com/articles/can ... -variables

Cheers,
Brent