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题库 / Prep2007E2-DS-22
Is ~$\frac{1}{p}> \frac{r}{r^{2}+2}$~
(1) p = r
(2) r > 0
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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在恒等变形的过程中，要考虑r的正负性会改变不等号的方向
r如果小于0，移项到右边会改变不等号的方向，所以A不对；
(1) p=rp=r --> 1r>rr2+2?1r>rr2+2? --> as r2+2r2+2 is always positive, multiplying inequality by this expression we'll get: r2+2r>r?r2+2r>r? --> r+2r>r?r+2r>r? --> 2r>0?2r>0?. This inequality is true when r>0r>0 and not true when r0. Not sufficient by itself.
(1)+(2) As from (2) r>0r>0, then 2r>02r>0 is true. Sufficient.
Answer: C.