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# If x y and z are positive is xz = 7xy ?

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Manager
Joined: 21 Jun 2011
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Location: United States
Concentration: Accounting, Finance
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If x y and z are positive is xz = 7xy ? [#permalink]

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Updated on: 27 Oct 2014, 02:28
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If x y and z are positive is xz = 7xy ?

(1) z/y = 7
(2) x/y = 1

I am getting OA as D if I subsititute x=y, I get $$yz=7y^2=>z=7y$$
What am I missing here
[Reveal] Spoiler: OA

Originally posted by davidfrank on 26 Oct 2014, 17:23.
Last edited by Bunuel on 27 Oct 2014, 02:28, edited 1 time in total.
Renamed the topic and edited the question.
Manager
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Posts: 108
Re: If x y and z are positive is xz = 7xy ? [#permalink]

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26 Oct 2014, 20:49
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To solve such type of questions we need to simplify the final question as much as possible

we need to find if xz=7xy ?

Simplifying the equation:
xz-7xy=0
x(z-7y)=0

If the options give us answers which state ,x=0 or z=7y then we can conclude that xz=7y.
Given x =positive so we need to find z=7y.

Option A : z/y=7 or z=7y ... as x,y and z are positive we know that x cannot be zero
So A is sufficient

Option B: x/y=1, as we dont know z we cannot prove xz=7xy as z is an unknown quantity.
So B insufficient
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Posts: 44592
Re: If x y and z are positive is xz = 7xy ? [#permalink]

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27 Oct 2014, 02:33
If x y and z are positive is xz = 7xy ?

(1) z/y = 7 --> z = 7y. Substitute the value of z in the question: is x(7y) = 7xy. Since LHS and RHS are the same then the answer to the question is YES. Sufficient.

(2) x/y = 1 --> x = y. Substitute the value of y in the question: is xz = 7x^2 ? --> is z = 7x ? Since we cannot answer this question neither with a definite YES nor with a definite NO, the statements is not sufficient.

Hope it's clear.
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If x y and z are positive is xz = 7xy ? [#permalink]

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10 Dec 2014, 16:12
As we know that x is positive, we can divide by x. So the question becomes is z=7y?

(1): z/y=7 ---> z=7y SUFFICIENT
(2): x/y=1 ---> x=y --> even if you Substitute x for y, you are still left with "is z=7x?" --> INSUFFICIENT
Manager
Joined: 21 Feb 2012
Posts: 59
Re: If x y and z are positive is xz = 7xy ? [#permalink]

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11 Dec 2014, 02:17
My approach (generally speaking)

Whenever we see common terms on LHS & RHS even if they are +ve we shouldn't be in a hurry to cancel them. Set up the equation first.

xz=7xy
x(z-7y)=0
so solution is
either x=0 or z=7y
so from statement 1 we get z=7y. so sufficient
from statement 2 we don't get anything. Insufficient.

The essence in these equations/inequalities is to know the solution set and work around/from that.
my 2 cents.
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J

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Manager
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Posts: 91
Re: If x y and z are positive is xz = 7xy ? [#permalink]

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10 Apr 2016, 20:45
Bunuel wrote:
If x y and z are positive is xz = 7xy ?

(1) z/y = 7 --> z = 7y. Substitute the value of z in the question: is x(7y) = 7xy. Since LHS and RHS are the same then the answer to the question is YES. Sufficient.

(2) x/y = 1 --> x = y. Substitute the value of y in the question: is xz = 7x^2 ? --> is z = 7x ? Since we cannot answer this question neither with a definite YES nor with a definite NO, the statements is not sufficient.

Hope it's clear.

Hi Bunuel,

If the question stem were stated as x,y,z are non negative, then would the answer be still A?
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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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11 Apr 2016, 00:04
Alok322 wrote:
Bunuel wrote:
If x y and z are positive is xz = 7xy ?

(1) z/y = 7 --> z = 7y. Substitute the value of z in the question: is x(7y) = 7xy. Since LHS and RHS are the same then the answer to the question is YES. Sufficient.

(2) x/y = 1 --> x = y. Substitute the value of y in the question: is xz = 7x^2 ? --> is z = 7x ? Since we cannot answer this question neither with a definite YES nor with a definite NO, the statements is not sufficient.

Hope it's clear.

Hi Bunuel,

If the question stem were stated as x,y,z are non negative, then would the answer be still A?

Yes. From (1) z/y = 7, means that neither z nor y is 0. So, we'd still have the same case.
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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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11 Apr 2016, 00:43
davidfrank wrote:
If x y and z are positive is xz = 7xy ?

(1) z/y = 7
(2) x/y = 1

I am getting OA as D if I subsititute x=y, I get $$yz=7y^2=>z=7y$$
What am I missing here

whenever you see all variables involved in an equation are positive you can reduce the variables if presented on both the side.

xz = 7xy -- divide by x
z = 7y

stmt1:

z/y = 7 i.e. z=7y

stmt:2
x/y =1 ... nothing is told about z.

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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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12 Aug 2016, 08:36
Hi all,

First post here. I have been lurking for a while, never had to post because the solutions were always great!

I am a bit stumped here in this question though. I know I'm doing something silly. If someone can please shed some light on what I'm doing wrong...

I chose D because, when you arrive at x = y, I just replaced x in the original stem by y. So I get zy=7y^2 and then on cancelling I come to z=7y.

Math Expert
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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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12 Aug 2016, 08:41
Neeraj91 wrote:
Hi all,

First post here. I have been lurking for a while, never had to post because the solutions were always great!

I am a bit stumped here in this question though. I know I'm doing something silly. If someone can please shed some light on what I'm doing wrong...

I chose D because, when you arrive at x = y, I just replaced x in the original stem by y. So I get zy=7y^2 and then on cancelling I come to z=7y.

Please check here: if-x-y-and-z-are-positive-is-xz-7xy-187488.html#p1433632 When you substitute x with y in the question, the question becomes "is z = 7x ?" Since we cannot answer this question neither with a definite YES nor with a definite NO, the statements is not sufficient.
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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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22 Jul 2017, 03:20
davidfrank wrote:
If x y and z are positive is xz = 7xy ?

(1) z/y = 7
(2) x/y = 1

I am getting OA as D if I subsititute x=y, I get $$yz=7y^2=>z=7y$$
What am I missing here

given xz = 7xy
divide the equation by x,, gives z = 7y

stat 1: z= 7y...suff

stat 2 : x = y..not suff

ans A
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Re: If x y and z are positive is xz = 7xy ? [#permalink]

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28 Sep 2017, 13:24
Expert's post
Top Contributor
davidfrank wrote:
If x y and z are positive is xz = 7xy ?

(1) z/y = 7
(2) x/y = 1

Target question: Is xz = 7xy ?
This is a good candidate for rephrasing the target question.

Since we're told that x is positive, we can take the equation xz = 7xy and divide both sides by x to get an EQUIVALENT equation: z = 7y
This allows us to REPHRASE the target question and ask an easier question....
REPHRASED target question: Is z = 7y ?

Statement 1: z/y = 7
Multiply both sides by y to get: z = 7y
Perfect - the answer to our REPHRASED target question is "Yes, z DOES equal 7y"
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x/y = 1
Keep in mind that our REPHRASED target question asks "Is z = 7y ?"
Since statement 2 provides no information about z, we cannot determine whether or not z = 7y
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

[Reveal] Spoiler:
A

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Re: If x y and z are positive is xz = 7xy ?   [#permalink] 28 Sep 2017, 13:24
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