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# What is the value of xy?

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
What is the value of xy?  [#permalink]

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12 Jul 2014, 15:09
3
9
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:10) correct 47% (01:50) wrong based on 266 sessions

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What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$

(2) $$xy>-9.5$$

Kudos for a correct solution.

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Posts: 52294
What is the value of xy?  [#permalink]

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12 Jul 2014, 15:09
4
1
SOLUTION

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$. This is the same as $$(xy)^2+2xy\pi-3\pi^2 = 0$$.

Solve for $$xy$$ (you can denote $$xy$$ as $$a$$ and solve quadratics) or factor: $$(xy+3\pi)(xy-\pi)=0$$. This means that $$xy=-3\pi$$ or $$xy=\pi$$. Not sufficient.

(2) $$xy>-9.5$$. Clearly insufficient.

(1)+(2) From (1) $$xy=-3\pi\approx{-9.45}$$ or $$xy=\pi\approx{3.14}$$. Both of these values are more than -9.5 (both of them satisfy the second statement), hence both of them are valid. Not sufficient.

Try NEW Algebra PS question.
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Re: What is the value of xy?  [#permalink]

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12 Jul 2014, 23:15
1
For me - E
1. NS - because of values of x and y
2. NS - because even if i square both sides i get xy>9.5, so inconclusive

Combining 1 and 2 and solving for xy - again non conclusive. As x^2*y^2 > 9.5^2

So E, according to me...

Glad if someone can feed in the right solution. It got me worried for a bit.

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+1, if you like this.
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Re: What is the value of xy?  [#permalink]

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13 Jul 2014, 01:10
Bunuel wrote:

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$

(2) $$xy>-9.5$$

Kudos for a correct solution.

Statement 1 :
$$x^2y^2+2xy\pi-3\pi^2 = 0$$
(xy)^2+2xypi-(3^0.5.pi)^2=0
(xy+3^0.5pi)^2-6pi^2=0
(xy+3^0.5pi)^2=6pi^2
Take square root on both the sides
|xy+3^0.5pi|=6^0.5pi
Since RHS can only be a positive number, LHS has to be a positive number
xy+3^0.5pi=6^0.5pi
xy=3^0.5pi(1+2^0.5)

We can have a definite value of xy.

Statement 2:
xy>-9.5
Insufficient

Ans=A

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Re: What is the value of xy?  [#permalink]

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13 Jul 2014, 01:17
3
Bunuel wrote:

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$

(2) $$xy>-9.5$$

Kudos for a correct solution.

st.1
$$x^2y^2+2xy\pi-3\pi^2 = 0$$

let xy=k

then we will have; $$k^2+2k\pi-3\pi^2 = 0$$

after factorization we have, $$(k+3\pi)(k-\pi)=0$$
thus k= xy = $$-3\pi and \pi$$

thus statement 1 alone is not sufficient

st.2 clearly not sufficient, as xy can be both positive as well as negative.

combining 1 and 2

xy= $$-3\pi$$ ~ -9.428
xy= $$\pi$$ ~ 3.142

as both of these values satisfy the inequality xy>-9.5

hence statement 1 and 2 together are not sufficient. thus answer should be E
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Re: What is the value of xy?  [#permalink]

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14 Jul 2014, 22:33
1
Bunuel wrote:

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$

(2) $$xy>-9.5$$

Kudos for a correct solution.

Statement 1:Not Sufficient
$$x^2y^2+2xy\pi-3\pi^2 = 0$$
$$(xy+3\pi)(xy-\pi)=0$$
$$xy=-3\pi$$ or $$xy=\pi$$

Statement 2: Clearly Not Sufficient

Statement 1 & 2: Not sufficient
Both $$xy=-3\pi$$ (approximately -9.42) and $$xy=\pi$$ fall within the $$xy>-9.5$$ criteria.

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: What is the value of xy?  [#permalink]

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15 Jul 2014, 09:41
SOLUTION

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$. This is the same as $$(xy)^2+2xy\pi-3\pi^2 = 0$$.

Solve for $$xy$$ (you can denote $$xy$$ as $$a$$ and solve quadratics) or factor: $$(xy+3\pi)(xy-\pi)=0$$. This means that $$xy=-3\pi$$ or $$xy=\pi$$. Not sufficient.

(2) $$xy>-9.5$$. Clearly insufficient.

(1)+(2) From (1) $$xy=-3\pi\approx{-9.45}$$ or $$xy=\pi\approx{3.14}$$. Both of these values are more than -9.5 (both of them satisfy the second statement), hence both of them are valid. Not sufficient.

Kudos points given to correct solutions.

Try NEW Algebra PS question.
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What is the value of xy?  [#permalink]

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13 Mar 2016, 08:36
Question, can someone show me the algebraic identity being used here, please? Is this a difference of squares?..
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: What is the value of xy?  [#permalink]

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13 Mar 2016, 08:42
iliavko wrote:
Question, can someone show me the algebraic identity being used here, please? Is this a difference of squares?..

It's done by factoring quadratics or by solving quadratics for xy.

Theory on Algebra: algebra-101576.html
Algebra - Tips and hints: algebra-tips-and-hints-175003.html

DS Algebra Questions to practice: search.php?search_id=tag&tag_id=29
PS Algebra Questions to practice: search.php?search_id=tag&tag_id=50

Special algebra set: new-algebra-set-149349.html

Hope this helps.
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Re: What is the value of xy?  [#permalink]

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28 Dec 2017, 08:38
Bunuel wrote:

What is the value of $$xy?$$

(1) $$x^2y^2+2xy\pi-3\pi^2 = 0$$

(2) $$xy>-9.5$$

Kudos for a correct solution.

Took 9+ min to solve this, BUT happy could do it of my own. Sharing my analysis..

Find 'xy'

Statement 1 $$x^2y^2+2xy\pi-3\pi^2=0$$
=> Let xy=m , substituting in the above equ
=> $$m^2+2m\pi-3\pi^2=0$$
=> or $$m^2+2m\pi-4\pi^2+\pi^2=0$$
=> $$(m^2+2m\pi+\pi^2)-4\pi^2=0$$
=> $$(m+\pi)^2-4\pi^2=0$$
=> $$(m+\pi)^2-(2\pi)^2=0$$
=> $$(m+\pi-2\pi)(m+\pi+2\pi)=0$$ ---- from$$(a^2-b^2)=(a-b)(a+b)$$
=> $$(m-\pi)(m+3\pi)=0$$
=> $$m=\pi$$ or $$-3\pi$$
=> i.e $$xy=\pi$$ or $$-3\pi$$
=> Since 2 values of 'xy'. Therefore Stat 1 NOT SUFFICIENT

Statement 2 xy>-9.5
=> 'xy' can have any value > -9.5 i.e -9.4, -9.1 ...etc
=> Therefore NOT SUFFICIENT

BOTH Stat 1 & 2
=> 'xy'= 3.14 or -9.42 from Stat 1
=> xy>-9.5 from stat 2
=> AGAIN 'xy' has 2 values. Therefore NOT SUFFICIENT

Therefore 'E'

Thanks
Dinesh
Re: What is the value of xy? &nbs [#permalink] 28 Dec 2017, 08:38
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# What is the value of xy?

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