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# The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:

The fastest way to solve this problem is first to recognize that an algebraic approach will take a little time. Essentially, we will have to multiply through by the product (x – 2)(x + 2)(x – 1), then simplify.

If, instead, we glance at the answer choices, we see that 3 of them make one of the denominators zero, a result that is not allowed (we cannot divide by zero). Specifically, x cannot be –2 because one denominator is x + 2; likewise, x cannot be 1 or 2, since we have x – 1 and x – 2 as denominators as well.

Thus, the only two possible answers are –1 and 0. We try each in turn.

If x = –1, then we have the following:

1/(–3) = 1/(1) + 1/(–2)?

–1/3 = 1 – 1/2?

This is not true.

However, if x = 0, then we have the following:

1/(–2) = 1/(2) + 1/(–1)?

–1/2 = 1/2 – 1?

–1/2 = –1/2?

This is true, so x can be equal to 0.

Alternatively, we could take the algebraic approach.

First, we multiply through by the product (x – 2)(x + 2)(x – 1) to eliminate denominators.

(x – 1)(x + 2) = (x – 2)(x – 1) + (x – 2)(x + 2)

x2 + x – 2 = x2 – 3x + 2 + x2 – 4

0 = x2 – 4x

0 = x(x – 4)

x = 0 or x = 4

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