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What is the value of xy?

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What is the value of xy? [#permalink]

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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.

[Reveal] Spoiler: OA

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What is the value of xy? [#permalink]

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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.

Answer: E.

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

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New post 12 Jul 2014, 23:15
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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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Re: What is the value of xy? [#permalink]

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New post 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

OA please.

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

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New post 13 Jul 2014, 01:17
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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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New post 14 Jul 2014, 22:33
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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.

Answer is E

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

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New post 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.

Answer: E.

Kudos points given to correct solutions.

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What is the value of xy? [#permalink]

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New post 13 Mar 2016, 08:36
Question, can someone show me the algebraic identity being used here, please? Is this a difference of squares?..

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

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New post 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.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm
Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

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] 24 Nov 2017, 10:32
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