financeguy25 wrote:
What is the value of \(\frac{x}{yz}\)?
(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\)
(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\)
DS86602.01
Target question: What is the value of x/yz? Statement 1: x = y/2 and z = 2x/5Take x = y/2 and multiply both sides by 2 to get:
2x = yAlso given:
z = 2x/5This allows us to take our target expression, x/yz, and replace y and z to get: x/yz = x/[(
2x)(
2x/5)]
= x/(4x²/5)
= (x)(5/4x²)
= 5x/4x²
= 5/4x
Since x can be any value, we can see that we cannot answer the
target question with certainty
Statement 1 is NOT SUFFICIENT
Statement 2: x/z = 5/2 and 1/y = 1/10[ Important: we are trying to find the value of x/yz
Notice that we can take x/yz and rewrite it as (x/z)(1/y), which works nicely with our given information.
We get:
x/yz = (x/z)(1/y) = (5/2)(1/10) = 5/20 = 1/4Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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