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## Comment on

Useful Contradictions## I am quite new to algebra

## Yes, you are correct. The

Yes, you are correct. The purpose of the video is to demonstrate that the properties of DS questions can help you identify errors that test-takers may make. So, at 2:55, we use this property to identify our mistake and then correct our factorization.

## There is a mistake in the

## Yes, the mistake was made

The "mistake" was made intentionally to show how a certain property of Data Sufficiency questions can help us identify errors we might make in our calculations.

So, in statement 1, we conclude that x = -2 or x = -3.

In statement 2, we conclude (incorrectly) that x = 4 or x = 6.

Since we arrive at CONTRADICTORY results, we know that we must have made a mistake in one of our calculations, and we can re-check our work to see where we erred.

So, around 2:50 in the video, we use this property to identify our mistake and correct our factorization.

## But, it can also be the case

## The statements will NEVER

The statements will NEVER contradict each other. So, if it seems like there's a contradiction, then we can be certain that the test-taker made an error.

## Hello, excellent course! Just

If we can assume that both sentences are always true and they do not contradict each other, couldn't we conclude that since they're both ecuations in function of X with only variable they both must be sufficient to determine the value of X, independently of one another?

Thank you,

## Not always.

Not always.

Consider this example:

What is the value of x?

(1) 2x = 6

(2) x² = 9

Both statements are true, but only one statement (statement 1) is sufficient to answer the target question alone.

## for your last comment 2nd sep

## You're referring to the

You're referring to the question:

What is the value of x?

(1) 2x = 6

(2) x² = 9

Statement 1 is sufficient because there is only one possible solution: x = 3

Statement 2 is not sufficient because there are two possible solutions: x = 3 and x = -3

Notice that 3² = 9 and (-3)² = 9

Does that help?

Cheers,

Brent

## Wouldn't it be a waste of

## Great question, Max!

Great question, Max!

There are A few IF's in your proposed rule that we should examine, but, in short, we can say:

If each quadratic equation yields two DIFFERENT possible x-values, and if the two quadratic equations do not yield the SAME two possible x-values, then the correct answer must be C.

However, there are different things that can mess up this rule. Here are two examples:

If x > 0, what is the value of x?

(1) x² + x - 6 = 0

Solving this quadratic, we see that EITHER x = 2 OR x = -3

Since we're told x > 0, we can be certain that x = 2

So, statement 1 is sufficient on its own.

------------------------------------------------

What is the value of x?

(1) x² - 6x + 9 = 0

(2) x² + 2x - 15 = 0

Factoring (1), we get: (x - 3)(x - 3) = 0

So, it MUST be the case that x = 3

So, statement 1 is sufficient on its own.

Factoring (2), we get: (x - 3)(x + 5) = 0

So, EITHER x = 3 OR x = -5

So, statement 2 is NOT sufficient on its own.

-------------------------------------------------

I like you're proposed rule, just as long as you're aware of a few potential loopholes.

Cheers,

Brent

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