Lesson: Common GMAT Data Sufficiency Myths - Part II

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Comment on Common GMAT Data Sufficiency Myths - Part II

hello again :)

another question, when we are dealing with a quadratic and we know that only positive numbers fulfil our conditions (for instance in geometry), could we skip the calculation in this case? or is it also possible to get 2 positive solution from a quadratic ?
gmat-admin's picture

Yes, it's possible to get to two positive solutions to a quadratic equation.

Take, for example, x² - 5x - 6 = 0
Factor to get: (x - 2)(x - 3) = 0
So, x = 2 or x = 3


Hello admin... From the question x and y are both positive integers how did u take x and y as 1
gmat-admin's picture

Is this the question you're referring to: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-... ?

If so, I'm not sure what you are asking. I don't have x = 1 and y = 1 as a solution anywhere in my answer (https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-...)

Can you please elaborate on your question?


You assumed the statement is sufficient by taking x=1 and y=1 because the statement said x and y are positive integers. I think it is insufficient because you can have other positive integers that will make the equation not sufficient such as 2 ,3 4 etc. can you explain ?
gmat-admin's picture

I believe you're referring to the question that starts at 2:15 in the above video.

We're told that x and y are positive integers, and we want to determine the value of x.

STATEMENT 1 tells us that 10x + 5y = 15
When we simplify this equation, we get: 2x + y = 3

Keep in mind that, in Data Sufficiency questions, each statement is true, so it MUST be the case that 2x + y = 3

Since there is ONLY ONE pair of values that satisfy this equation (x = 1 and y = 1), we can be certain that x MUST EQUAL 1.

If you feel that x could have values other than 1, you must find a DIFFERENT pair of x and y values that satisfy the equation 2x + y = 3.

For example, you are suggesting that x could equal 2. However, in order to satisfy the given equation (2x + y = 3), we must find a POSITIVE value of y to go along with x = 2.
However, if x = 2, then y must equal -3, and -3 is not positive.

Does that help?


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