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# If xy = z, what is the value of y ?

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Math Expert
Joined: 02 Sep 2009
Posts: 49231
If xy = z, what is the value of y ?  [#permalink]

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25 Sep 2017, 23:58
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Difficulty:

55% (hard)

Question Stats:

26% (00:42) correct 74% (00:34) wrong based on 81 sessions

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If xy = z, what is the value of y ?

(1) x = 3z
(2) x > 1

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Joined: 25 Feb 2013
Posts: 1213
Location: India
GPA: 3.82
If xy = z, what is the value of y ?  [#permalink]

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26 Sep 2017, 00:24
1
Bunuel wrote:
If xy = z, what is the value of y ?

(1) x = 3z
(2) x > 1

Statement 1: substitute the value of $$x$$ in the equation to get $$3zy=z$$ or

$$3zy-z=0$$ or $$z(3y-1)=0$$, hence either $$z=0$$ or $$3y-1=0$$. Hence insufficient

Statement 2: nothing mentioned about $$y$$. Hence insufficient

Combining 1 & 2 it is clear that that $$x$$ is not $$0$$ so $$z$$ cannot be $$0$$.

Hence $$3y-1=0$$ or $$y =\frac{1}{3}$$. Sufficient

Option C
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Re: If xy = z, what is the value of y ?  [#permalink]

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26 Sep 2017, 17:25
1
niks18
Why is he statement 1 insufficient? We are not suppose to find the value of z, we have to find the value of y.
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Re: If xy = z, what is the value of y ?  [#permalink]

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26 Sep 2017, 17:48
niks18 wrote:
Bunuel wrote:
If xy = z, what is the value of y ?

(1) x = 3z
(2) x > 1

Statement 1: substitute the value of $$x$$ in the equation to get $$3zy=z$$ or

$$3zy-z=0$$ or $$z(3y-1)=0$$, hence either $$z=0$$ or $$3y-1=0$$. Hence insufficient

Statement 2: nothing mentioned about $$y$$. Hence insufficient

Combining 1 & 2 it is clear that that $$x$$ is not $$0$$ so $$z$$ cannot be $$0$$.

Hence $$3y-1=0$$ or $$y =\frac{1}{3}$$. Sufficient

Option C

Wait...what? Why? Substituting x=3z gives us the value of y as 1/3 with statement 1. Answer is A no?
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Re: If xy = z, what is the value of y ?  [#permalink]

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26 Sep 2017, 21:03
1
manik919 wrote:
niks18
Why is he statement 1 insufficient? We are not suppose to find the value of z, we have to find the value of y.

Hi manik919 & sasyaharry

What happens if z=0? then y can have any number. You cannot get a unique value of y unless you are sure that z is not equal to 0.
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If xy = z, what is the value of y ?  [#permalink]

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27 Sep 2017, 05:05
1
Bunuel wrote:
If xy = z, what is the value of y ?

(1) x = 3z
(2) x > 1

Another approach

In this question, any variable can take any number with any sign. There is no constraint on any variable.

(2) x > 1

No info about z or relations

Insufficient

(1) x = 3z.........$$z =\frac{1}{3} x$$

Substitute in $$xy = z$$

$$x y = \frac{1}{3} x$$

case 1: Let x = 0.........LHS = RHS =0 ....then y can take any number. y could be 0, 1, -10, 1000...etc

case 2: Let x = any number other than 0........ then x canceled out from both sides............ Always y = 1/3

Insufficient

Combine 1 & 2

from statement 2: x > 1...it means case 2 only in statement 1 achieved.

Clearly $$y = \frac{1}{3}$$

P.S.: niks18 did the right way. My first solution was like you. Kudos to your answer.
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If xy = z, what is the value of y ?  [#permalink]

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01 Oct 2017, 14:21
Bunuel wrote:
If xy = z, what is the value of y ?

(1) x = 3z
(2) x > 1

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variable and 1 equation. Thus C could be the answer most likely.

Condition 1)
Since $$x = 3z$$ and $$xy = z$$, we have $$3zy = z$$ or $$z(3y-1) = 0$$.
Then $$z = 0$$ or $$y = 1/3$$
Thus we have solutions $$y = 1$$, $$z = 1$$ and $$y = 1/3$$, $$z = 1$$
The answers are not unique. This condition alone is not sufficient.

Condition 2)
Since $$x > 1$$ and $$y = z/x$$, we can't identify the value of $$y$$.
This condifition alone is not sufficient, either.

Condition 1) & 2)
Since $$x = 3z$$ and $$xy = z$$, we have $$3zy = z$$ or $$z(3y-1) = 0$$.
$$z = 0$$ or $$y = 1/3$$
However, $$z$$ cannot be zero since $$x = 3z$$ and $$x > 1$$.

Thus $$y = 1/3$$.
Both conditions together are sufficient.

Therefore, C is the answer as expected.
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