SpiritualYoda wrote:
A, B, R and S are four positive numbers. Does AS = BR?
Statement #1: \(\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}\)
Statement #2: In the x-y plane, the line through (A, B) and (R, S) goes through the origin
Statement 1:Case 1: A=1, B=2, R=1, and S=2, with the result that \(A^2+B^2=5\) and \(R^2+S^2=5\)
In this case, AS=2 and BR=2, so the answer to the question stem is YES.
Case 2: A=1, B=2, R=2, and S=1, with the result that \(A^2+B^2 = 5\) and \(R^2+S^2=5\)
In this case, AS=1 and BR=4, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2:Slope yielded by (A, B) and (0, 0) \(= \frac{B-0}{A-0} = \frac{B}{A}\)
Slope yielded by (R, S) and (0, 0) \(= \frac{S-0}{R-0} = \frac{S}{R}\)
Since the slope in each case must be THE SAME, we get:
\(\frac{B}{A} = \frac{S}{R}\)
\(AS=BR\)
Thus, the answer to the question stem is YES.
SUFFICIENT.
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