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

Question

If xy = z, what is the value of y ?
 
(1) x = 3z
(2) x > 1

niks18 · Answer

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

manik919 · Answer

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.

sasyaharry · Answer

Wait...what? Why? Substituting x=3z gives us the value of y as 1/3 with statement 1. Answer is A no?

niks18 · Answer

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.

Mo2men · Answer

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}

Answer C

P.S.:  niks18  did the right way. My first solution was like you. Kudos to your answer.

MathRevolution · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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