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.

for your last comment 2nd sep 2017 X^2=9 is sufficient as we know 3^2=9.Plesae let me know if I am considering any thing wrong.
gmat-admin's picture

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?


Wouldn't it be a waste of time to solve both equations? If we know that each statement provides us with 2 possible answers for x (eliminating A,B & D), and we also know that the 2 statements cannot contradict each other, can't we conclude that the correct answer is C? Unless you're saying there are cases where 2 different quadratic equations can give us the same 2 values of x (keeping answer "E" relevant) and the only way to find out is by solving both equations. If so, can you provide an example?
gmat-admin's picture

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.


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