BTGmoderatorDC wrote:If a < b , is a > 0 ?
(1) \(a^2 < b^2\)
(2) \(a^2 < ab < b^2\)
OA B
Source: Veritas Prep
Let's take each statement one by one.
(1) \(a^2 < b^2\)
Case 1: Say a = 1 and b = 2, then 1^1 < 2^2 => 1 < 4. The answer is yes.
Case 2: Say a = -1 and b = 2, then (-1)^1 < 2^2 => 1 < 4. The answer is no.
No unique answer. Insufficient.
(2) \(a^2 < ab < b^2\)
Case 1: Say a > 0, then from \(a^2 < ab\), we can cancel a from both sides. \(a < b\). The answer is yes.
Case 2: Say a < 0, then from \(a^2 < ab\), we can cancel a from both sides but we'll have to reverse the sign of the equality since a is negative. Thus, \(a > b\). However, this is not possible since it is given that \(a < b\).
Thus, a > 0. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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