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Statement 1: ab < 2 Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a. When we do this we get: b < 2/a Since a > 2, we know that the fraction's denominator is greater its numerator, which means 2/a must be less than 1 So, 2/a < 1 Since b < 2/a, we get: b < 2/a < 1 In other words, b < 1 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ab > 0 Let's TEST some numbers. There are several values of a and b that satisfy statement 2. Here are two: Case a: a = 3 and b = 2, in which case b > 1 Case b: a = 3 and b = 0.1, in which case b < 1 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

We are given that a > 2 and need to determine whether b < 1.

Statement One Alone:

a·b < 2

Let’s divide each side by a. Note that since a > 2, a is positive, and so the inequality sign will not be reversed:

b < 2/a

2/a is a fraction in which the denominator is greater than the numerator. Thus, 2/a < 1 and b < 2/a < 1. Statement one is sufficient to answer the question.

Statement Two Alone:

a·b > 0

The information in statement two is not sufficient to answer the question. For example, if a = 3 and b = 1/2, then b is less than 1; however, if a = 3 and b = 3, then b is not less than 1.

Answer: A
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Statement 1: ab < 2 Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a. When we do this we get: b < 2/a Since a > 2, we know that the fraction's denominator is greater its numerator, which means 2/a must be less than 1 So, 2/a < 1 Since b < 2/a, we get: b < 2/a < 1 In other words, b < 1 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Hi Brent,

Can we not use a similar approach on Statement 2?

Statement 2: ab > 0 Since we're told that a > 2, we know that a is POSITIVE, which means we can safely divide both sides of the inequality by a. When we do this we get: b > 0

Since we cannot answer the target question with certainty, statement 2 is INSUFFICIENT