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# What is the value of x/(yz) ?

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Re: What is the value of x/(yz) ? [#permalink]
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What is the value of x/(yz) ?

(1) x = y/2 and z = 2x/5
(2) x/z = 5/2 and 1/y = 1/10

Sol: St 1---> x=2y and z=2x/5 or 4y/5
Thus we have 2y/(y*4y/5) or 10y/4y^2---> 10/4y but we don't the value of y so not sufficient

St 2: x=5/2z and y=10
Subsituting we get (5z/2)/10*z or 5z/20z or 1/4
Ans B
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Re: What is the value of x/(yz) ? [#permalink]
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Option B:
From S1: replacing y=2x and z=2x/5 does not give a value for x/(yz)
Not sufficient

From S2: x/z * 1/y are both given
So value=1/4
Sufficient
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Re: What is the value of x/(yz) ? [#permalink]
Bunuel wrote:
SOLUTION

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.

In statement 1.......I tried to solve it through algebra. y= 2x and z=2x/5 so if we pick up expression given in question and replace y and z with 2x and 2x/5 respectively......the entire expression would only have one variable(x).....by a little calculation all x in expressions would be cancelled with each others and we will get 4/5 as answer of expression. Than why sttment 1 is insufficient? can you please guide me?
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Re: What is the value of x/(yz) ? [#permalink]
mulhinmjavid wrote:
Bunuel wrote:
SOLUTION

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.

In statement 1.......I tried to solve it through algebra. y= 2x and z=2x/5 so if we pick up expression given in question and replace y and z with 2x and 2x/5 respectively......the entire expression would only have one variable(x).....by a little calculation all x in expressions would be cancelled with each others and we will get 4/5 as answer of expression. Than why sttment 1 is insufficient? can you please guide me?

When you substitute y = 2x and z = 2x/5 into x/(yz) you get 5/(4x). Without knowing the value of x we cannot get the value of 5/(4x).

Hope it's clear.
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Re: What is the value of x/(yz) ? [#permalink]
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 x/(yz) ? [#permalink]
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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/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

Cheers,
Brent
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Re: What is the value of x/(yz) ? [#permalink]
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

Statement - I (Insufficient)
1. $$x = \frac{y}{2}$$ can be written as $$\frac{x}{y} = \frac{1}{2}$$

2. Substituting $$\frac{x}{y} = \frac{1}{2}$$ and $$z = \frac{2x}{5}$$ in $$\frac{x}{yz}$$ we get $$\frac{1}{2} * \frac{5}{2x}$$

3. As we see, one variable is remains uncancelled and hence we cannot arrive at the final answer

Statement - II (Sufficient)
Substituting $$\frac{x}{z} = \frac{5}{2}$$ and $$\frac{1}{y} = \frac{1}{10}$$ in $$\frac{x}{yz}$$ we get $$\frac{5}{2}*\frac{1}{10} = \frac{1}{4}$$

Ans. B
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Re: What is the value of x/(yz) ? [#permalink]
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did anyone thought it was y^z instead of y*z at first?
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Re: What is the value of x/(yz) ? [#permalink]
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Re: What is the value of x/(yz) ? [#permalink]
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