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What is the value of x/(yz) ?

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Source: — Data Sufficiency |
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by Brent@GMATPrepNow » Fri Dec 20, 2019 5:15 am

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BTGmoderatorDC 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 \(\frac{1}{y} = \frac{1}{10}\)
Target question: What is the value of x/yz?

Statement 1: x = y/2 and z = 2x/5
Take x = y/2 and multiply both sides by 2 to get: 2x = y
Also given: z = 2x/5

This 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 = 1/4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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by deloitte247 » Sun Dec 22, 2019 2:20 am

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$$I.e\ what\ is\ \frac{x}{y}\cdot\frac{1}{z}$$
or
$$what\ is\ \frac{1}{y}\cdot\frac{z}{z}$$
Statement 1: x = y/2, and z = 2x/5
If x = y/2, then z = 2x/5
$$Therefore,\ \frac{x}{yx}=\frac{\frac{y}{2}}{2x\left(\frac{2x}{5}\right)}$$
$$\frac{x}{yx}=\frac{\frac{y}{2}}{\frac{4x^2}{5}}$$
$$\frac{x}{yx}=\frac{y}{2}\cdot\frac{5}{4x^2}$$
The exact value of 'y' and 'x' is unknown, hence, statement 1 is NOT SUFFICIENT.

Statement 2: x/z = 5/2, and 1/y = 1/10
Given that;
$$\frac{x}{yx}=\frac{1}{y}\cdot\frac{x}{z}$$
$$where\ \frac{1}{y}=\frac{1}{10}\ and\ \frac{x}{z}=\frac{5}{2}$$
$$then,\ \frac{x}{yz}=\frac{1}{10}\ \cdot\frac{5}{2}=\frac{1}{4}$$
$$\frac{x}{yz}=\frac{1}{4}$$
Statement 2 alone is SUFFICIENT.

Since only statement 2 alone is SUFFICIENT, then, option B is the correct answer.
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