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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