If ab ≠0, is ab > a/b ?
(1) |b| > 1
(2) ab + a/b > 0
ab > a/b?
ab - a/b > 0
ab²/b - a/b > 0
(ab² - a) / b > 0
[ (a)(b² - 1) ] / b > 0
(a/b)(b² - 1) > 0?
Question stem, rephrased: Are a/b and b² - 1 the SAME SIGN?
Statement 1: |b| > 1
Thus, b² - 1 > 0.
No information about a/b.
INSUFFICIENT.
Statement 2: ab + a/b > 0
ab²/b + a/b > 0
(ab² + a) / b > 0
[ (a)(b² + 1) ] / b > 0
(a/b)(b² + 1) > 0.
Since it is not possible for b² + 1 to be negative, the inequality above holds true only if a/b > 0.
No information about b² - 1.
INSUFFICIENT.
Statements combined:
Statement 1: b² - 1 > 0.
Statement 2: a/b > 0.
Thus, a/b and b² - 1 are the SAME SIGN.
SUFFICIENT.
The correct answer is
C.
Our target question is ab>a/b
we can rephrase and get b^2>1
When an inequality is multiplied or divided by a negative value, the direction of the inequality must FLIP.
Here, the signs of a and b are unknown.
Thus, if we multiply each side by b and divide each side by a, we cannot be certain whether the resulting inequality should be b²>1 or b²<1.
For this reason, it is safer to eschew algebra or to simplify as I did in my solution above.
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