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M27-10

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Joined: 02 Sep 2009
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16 Sep 2014, 00:27
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Difficulty:

25% (medium)

Question Stats:

71% (01:18) correct 29% (01:47) wrong based on 217 sessions

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If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

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16 Sep 2014, 00:27
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Official Solution:

(1) $$x^2*y=3$$. If $$x=1$$, then $$y=z=3$$ and $$yz=9$$; but if $$x=3$$, then $$y=\frac{1}{3}$$, $$z=1$$ and $$yz=\frac{1}{3}$$. Not sufficient.

(2) $$\sqrt{x*y^2}=3$$. Square this equation: $$x*y^2=9$$, re-write as: $$(xy)*y=9$$. Now, since $$xy=z$$ then: $$z*y=9$$. Sufficient.

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25 Jun 2016, 06:02
Bunuel wrote:
If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

Given $$xy=z$$ and asked us to find $$yz$$.

For equation $$xy=z$$ , multiplying y on both sides
=> $$xy^2$$ =$$yz$$ or $$yz$$ = $$xy^2$$.

Then we need to know the value of $$xy^2$$ ---> eq 1.

Stat 1: $$x^2*y=3$$

=> y = 3 / $$x^2$$ --> squaring... $$y^2$$ = 9 / $$x^4$$.

Then sub $$y^2$$ value in eq 1 , we get the result as 9 / $$x^3$$. We are not sure of x value. This is not sufficient.

Stat 2: Given $$\sqrt{x*y^2}$$ = 3.

Squaring on both side we get $$xy^2$$ = 9.

Then substituting in eq 1 , we get yz = 9. This is sufficient.

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Joined: 01 Jun 2016
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16 Sep 2016, 18:20
stat 2
should't be y an incognito, since y2 is module? we don't know the sing of y?
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16 Sep 2016, 23:14
mounirbr wrote:
stat 2
should't be y an incognito, since y2 is module? we don't know the sing of y?

Not sure I understand what you mean. Can you please tell me which step is unclear below?

(2) $$\sqrt{x*y^2}=3$$. Square this equation: $$x*y^2=9$$, re-write as: $$(xy)*y=9$$. Now, since $$xy=z$$ then: $$z*y=9$$. Sufficient.
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09 Nov 2017, 12:25
What if for st.2 x=1/3; y=3? then z=1
OR
x=1. y=3 then z=3

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09 Nov 2017, 20:18
Life! wrote:
What if for st.2 x=1/3; y=3? then z=1
OR
x=1. y=3 then z=3

How does x = 1/3 and y = 3 satisfy the second statement: $$\sqrt{x*y^2}=3$$?
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30 Dec 2017, 03:23
Bunuel wrote:
If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

Hi Bunuel.
Can we solve statement 2 in the way i mentioned below?

(2) $$\sqrt{x*y^2}=3$$

$$\sqrt{x}$$ * $$\sqrt{y^2}$$= 3 --> $$\sqrt{x}$$ * |y|= 3
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30 Dec 2017, 04:11
sandysilva wrote:
Bunuel wrote:
If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

Hi Bunuel.
Can we solve statement 2 in the way i mentioned below?

(2) $$\sqrt{x*y^2}=3$$

$$\sqrt{x}$$ * $$\sqrt{y^2}$$= 3 --> $$\sqrt{x}$$ * |y|= 3

No. You still need to square.
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20 Sep 2018, 08:51
Bunuel wrote:
If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

HI Bunnel, Is this 700 level question ? or 600-700 level question.
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20 Sep 2018, 19:50
MaheshDuggirala wrote:
Bunuel wrote:
If $$x \gt 0$$ and $$xy=z$$, what is the value of $$yz$$?

(1) $$x^2*y=3$$.

(2) $$\sqrt{x*y^2}=3$$.

HI Bunnel, Is this 700 level question ? or 600-700 level question.

According to the stats, which you can check in the first post, the difficulty level of the question is 700+.
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Re: M27-10 &nbs [#permalink] 20 Sep 2018, 19:50
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