Algebra - GMAT Quantitative

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Question

Consider the equation

How many real solutions does this equation have?

Statement 1: There exists two different real numbers such that and

Statement 2: is a positive integer.

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Answer

can be rewritten as

If Statement 1 holds, then the equation can be rewritten as . This equation has solution set , which comprises two real numbers.

If Statement 2 holds, the discriminant is positive, being the sum of a nonnegative number and a positive number; this makes the solution set one with two real numbers.

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