roastedchips wrote:

If a>b>0, is b <2?

1) 1/a >1/2

2) (1/a) + (1/b) =1

We are given that a > b > 0 and need to determine whether b < 2.

Statement One Alone:

1/a > 1/2

Taking the reciprocal of each side and reversing the direction of the inequality, we get:

a < 2

We see that a is less than 2, and thus b must also be less than 2. Statement one is sufficient to answer the question.

Statement Two Alone:

(1/a) + (1/b) = 1

Multiplying the entire inequality by ab (which is non-zero because a > b > 0), we have:

b + a = ab

b = ab - a

b = a(b - 1)

a = b/(b - 1)

Substituting for a in the inequality given in the question stem, a > b > 0, we have:

b/(b - 1) > b > 0

Since b > 0, we can divide each side of the inequality by b without changing the inequality sign:

1/(b - 1) > 1

Taking the reciprocal of each side and reversing the direction of the inequality, we get:

b - 1 < 1

b < 2

Statement two is sufficient to answer the question.

Answer: D

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