It is currently 19 Oct 2017, 09:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128871 [0], given: 12183

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

### Show Tags

25 Sep 2017, 23:58
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

18% (00:11) correct 82% (00:34) wrong based on 57 sessions

### HideShow timer Statistics

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

(1) x = 3z
(2) x > 1
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128871 [0], given: 12183

Senior Manager
Joined: 25 Feb 2013
Posts: 401

Kudos [?]: 170 [1], given: 31

Location: India
GPA: 3.82
If xy = z, what is the value of y ? [#permalink]

### Show Tags

26 Sep 2017, 00:24
1
KUDOS
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

Kudos [?]: 170 [1], given: 31

Intern
Joined: 16 Jul 2016
Posts: 12

Kudos [?]: 2 [1], given: 28

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

### Show Tags

26 Sep 2017, 17:25
1
KUDOS
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.

Kudos [?]: 2 [1], given: 28

Manager
Joined: 22 Nov 2016
Posts: 200

Kudos [?]: 37 [0], given: 38

Location: United States
GPA: 3.4
Re: If xy = z, what is the value of y ? [#permalink]

### Show Tags

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?
_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 37 [0], given: 38

Senior Manager
Joined: 25 Feb 2013
Posts: 401

Kudos [?]: 170 [1], given: 31

Location: India
GPA: 3.82
Re: If xy = z, what is the value of y ? [#permalink]

### Show Tags

26 Sep 2017, 21:03
1
KUDOS
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.

Kudos [?]: 170 [1], given: 31

VP
Joined: 26 Mar 2013
Posts: 1260

Kudos [?]: 285 [1], given: 163

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

### Show Tags

27 Sep 2017, 05:05
1
KUDOS
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.

Kudos [?]: 285 [1], given: 163

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4133

Kudos [?]: 2891 [0], given: 0

GPA: 3.82
If xy = z, what is the value of y ? [#permalink]

### Show Tags

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2891 [0], given: 0

If xy = z, what is the value of y ?   [#permalink] 01 Oct 2017, 14:21
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.