Lesson: Useful Contradictions

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I am quite new to algebra shouldn't it be -2x12 instead of -4x-6 around 2min.
gmat-admin's picture

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 mathematical calculation in the quadratic equation x^2 - 10x - 24 = 0; i think it was taken as x^2 - 10x + 24 = 0.. i request you to go through the video and rectify the same. Thank you
gmat-admin's picture

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 that if both statements were contradicting, the answer is E.
gmat-admin's picture

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 have a quick question:

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,
gmat-admin's picture

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.

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