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

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Thu Sep 28, 2017 6:34 am
Vincen wrote:If x y and z are positive is xz = 7xy ?

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

The OA is A.

I am getting OA as D. If I substitute x=y, I get yz=7y^2 => z=7y.
What am I missing here?
You made that substitution into a question. So what you have is the rephrased question: "Is z = 7y?" When you're looking at statement 2 alone, you have no information about z, so there's no way you could know this. If y = 1, and z = 7, the answer would be YES, z = 7y; but if y = 1 and z = 8, the answer would be NO, z is not equal to 7y, so statement 2 alone is not sufficient to answer the question.
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by Brent@GMATPrepNow » Thu Sep 28, 2017 12:24 pm
Vincen 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.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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