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(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.

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.
_________________

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.

(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.

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.
_________________

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