Bunuel wrote:

rxs0005 wrote:

If rs ≠ 0, does 1/r + 1/s = 1

(1) rs = 1

(2) s + r = 2.5

Did not understand the OA

Is \(\frac{1}{r}+\frac{1}{s}=1\)?

(1) rs = 1 --> \(s=\frac{1}{r}\) --> question becomes: is \(\frac{1}{r}+r=1\) --> is \(r^2-r+1=0\), no real \(r\) satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.

(2) s + r = 2.5 --> \(s=2.5-r\) --> question becomes: is \(\frac{1}{r}+\frac{1}{2.5-r}=1\) --> is \(2r^2-5r+5=0\), no real \(r\) satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.

Answer: D.

A simpler approach would be:

Question is whether -> 1/r + 1/s = 1 or r+s/rs=1....(eq.1)

Stmt 1 -> rs=1 , substituting in (eq.1)

r+s=1 or 1/r+1/s = 1 -> Sufficient

Stmt 1 -> s+r=2.5 , substituting in (eq.1)

2.5/rs=1 => rs=2.5

or 1/r+1/s = 1 -> Sufficient

Ans - D

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