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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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(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.
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