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

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

Answer: A.

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]
Expert Reply
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.

Answer: A.

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]
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.

Answer is A.
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Re: If x y and z are positive is xz = 7xy ? [#permalink]
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 help!
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Re: If x y and z are positive is xz = 7xy ? [#permalink]
Expert Reply
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 help!

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]
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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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

Answer:

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

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

(1) z/y = 7
z = 7y;
zx = 7xy
SUFFICIENT

(2) x/y = 1
x = y
zx = zy
NOT SUFFICIENT

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