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

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by M7MBA » Sat Apr 28, 2018 1:51 am

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

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

The OA is A.

Why is sufficient the first statement? May someone helps me here? I'd be thankful.
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Source: — Data Sufficiency |

by GMATGuruNY » Sat Apr 28, 2018 2:22 am
M7MBA wrote:If x y and z are positive is xz = 7xy?

(1) z/y = 7
(2) x/y = 1
Since x is positive, we can divide both sides of the question stem by x:
xz/x = 7xy/x
z =7y.
Questions stem, rephrased:
Does z = 7y?

Statement 1:
z/y = 7
z = 7y.
Thus, the answer to the question stem is YES.

Statement 2:
No information about z.
INSUFFICIENT.

The correct answer is A.
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by Vincen » Sat Apr 28, 2018 2:25 am
Hello gmat_mission.

(1) z/y = 7

This statement implies that z=7y. Therefore, $$xz=x\left(7y\right)=7xy.$$ Hence, the answer is YES. SUFFICIENT.

(2) x/y = 1

This statement tells us that x=y. Hence $$7xy=7x^2=7y^2.$$ Since we don't know anything about z, we don't know if xz=7xy. NOT SUFFICIENT.

Hence, the correct answer is the option A
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