Bunuel wrote:

Is 1/(a - b) < b + a?

(1) (a + b)(a – b) < 1

(2) ab > a – b

We need to determine whether 1/(a - b) < b + a, or equivalently, whether a + b > 1/(a - b).

Statement One Alone:(a + b)(a – b) < 1

If we divide both sides by a - b, we would have:

a + b < 1/(a - b) if a - b is positive,

OR

a + b > 1/(a - b) if a - b is negative.

Since we don’t know whether a - b is positive or negative, we can’t determine whether a + b > 1/(a - b) or a + b < 1/(a - b). Statement one alone is not sufficient to answer the question.

Statement Two Alone:ab > a – b

If a = 1 and b = 2, then 1/(a - b) < b + a since 1/-1 = -1 < 2 + 1 = 3. However, if a = 3/4 and b = 2/3, then 1/(a - b) > b + a since 1/(1/12) = 12 > 2/3 + 3/4. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:We can use the same examples as in statement two because both examples also satisfy statement one. If a = 1 and b = 2, (a + b)(a - b) = (3)(-1) = -3 < 1, and if a = 3/4 and b = 2/3, (a + b)(a - b) = (17/12)(1/12) = 17/144 < 1. However, in the former example, 1/(a - b) < b + a, and in the latter, 1/(a - b) > b + a. The two statements together are still not sufficient to answer the question.

Answer: E

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