ziyuen wrote:

Is \((\frac{a}{p})(p^2+r^2+s^2)=ap+br+cs\)?

(1) \(\frac{c}{s}=\frac{a}{p}\)

(2) \(\frac{a}{p}=\frac{b}{r}\)

\(\big ( \frac{a}{p} \big )(p^2+r^2+s^2) = ap +\frac{a }{p}\times r^2 + \frac{a }{p}\times s^2 \quad (*)\)

(1) \(\frac{c}{s}=\frac{a}{p}\)

\(\implies (*) = ap + \frac{a }{p}\times r^2 + \frac{c}{s}\times s^2 = ap + cs + \frac{a }{p}\times r^2\)

We can't know whether \(\frac{a }{p}\times r^2= br\) or not. Insufficient.

(2) \(\frac{a}{p}=\frac{b}{r}\)

\(\implies (*) = ap + \frac{b }{r}\times r^2 + \frac{a}{p}\times s^2 = ap + br + \frac{a }{p}\times s^2\)

We can't know whether \(\frac{a }{p}\times s^2= cs\) or not. Insufficient.

Combine (1) and (2) we have

\((1) = ap + \frac{b }{r}\times r^2 + \frac{c}{s}\times s^2 = ap + br + cs\). Sufficient.

The answer is C

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