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# What is the value of x/yz?

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Intern
Joined: 06 Feb 2009
Posts: 2
Schools: HBS
What is the value of x/yz?  [#permalink]

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Updated on: 02 Nov 2018, 03:15
1
3
00:00

Difficulty:

25% (medium)

Question Stats:

75% (00:59) correct 25% (01:03) wrong based on 412 sessions

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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 $$\frac{1}{y} = \frac{1}{10}$$

Originally posted by financeguy25 on 08 Mar 2009, 18:28.
Last edited by Bunuel on 02 Nov 2018, 03:15, edited 2 times in total.
EDITED.
Math Expert
Joined: 02 Sep 2009
Posts: 51121
What is the value of x/yz?  [#permalink]

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05 Jul 2013, 03:40
What is the value of x/yz?

(1) $$x = \frac{y}{2}$$ and $$z = \frac{2x}{5}$$. If $$y=10$$, then $$x=5$$, $$z=2$$ and in this case $$\frac{x}{yz}=\frac{5}{20}=\frac{1}{4}$$ BUT if $$y=20$$, then $$x=10$$, $$z=4$$ and in this case $$\frac{x}{yz}=\frac{10}{80}=\frac{1}{8}$$. Not sufficient.

(2) $$\frac{x}{z} = \frac{5}{2}$$ and $$\frac{1}{y} = \frac{1}{10}$$. Multiply these two equations: $$\frac{x}{yz}=\frac{5}{20}$$. Sufficient.

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Re: What is the value of  [#permalink]

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02 Nov 2018, 03:16
carcass 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 $$\frac{1}{y} = \frac{1}{10}$$

We'll try to simplify and rearrange our data to create x/yz.
This is a Precise approach.

(1) we have x = y/2 --> x/y = 1/2. Multiplying by z = 2x/5 gives xz/y = (2x^2)/(5y), which can have many different values.
Insufficient.

(2) multiplying x/z = 5/2 by 1/y = 1/10 gives x/yz = 5/20, a unique value.
Sufficient.

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Re: What is the value of &nbs [#permalink] 02 Nov 2018, 03:16
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