Is x/p(p^2 + q^2 + r^2) = xp + yq + zr ?

Question

Is  \frac{x}{p}(p^2+q^2+r^2) = xp+yq+zr?

(1)  \frac{z}{r}=\frac{x}{p}

(2)  \frac{x}{p}=\frac{y}{q}

IanStewart · Answer

If we expand the brackets on the left side of the question, the question becomes:

Is (x/p)(p^2) + (x/p)(q^2) + (x/p)(r^2) = xp + yq + zr ?

Using Statement 1, we can replace the "x/p" in front of the "r^2" with "z/r", and using Statement 2 we can replace the "x/p" in front of the "q^2" with "y/q". So the question then becomes

Is (x/p)(p^2) + (y/q)(q^2) + (z/r)(r^2) = xp + yq + zr ?

and cancelling the denominators on the left side, we immediately see the left and right sides are identical. So the answer is C, since each statement is clearly insufficient alone.

bumpbot · Answer

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Is x/p(p^2 + q^2 + r^2) = xp + yq + zr ?

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