What is the value of xy?

Question

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What is the value of  xy?

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

(2)  xy>-9.5

Bunuel · Accepted Answer

SOLUTION

What is the value of  xy ? 
 
(1)  x^2y^2+2xy\pi-3\pi^2 = 0 . 
 
This can be expressed as:  (xy)^2 + 2xy\pi - 3\pi^2 = 0 .
 
To find the value of  xy , we can either directly solve the quadratic for  xy  (to simplify, we can denote  xy  as  a  to get  a^2 + 2a\pi - 3\pi^2 = 0  and solve for  a ), or factor  (xy)^2 + 2xy\pi - 3\pi^2 = 0 : 
 
 (xy)^2 + 3xy\pi - xy\pi - 3\pi^2 = 0 
 
 (xy)(xy + 3\pi) - \pi(xy + 3\pi) = 0 
 
 (xy+3\pi)(xy-\pi)=0 
 
This gives us two possible solutions:  xy=-3\pi  or  xy=\pi . This statement is not sufficient to determine a unique solution.
 
(2)  xy>-9.5 . 
 
Clearly insufficient.
 
(1)+(2) From (1), we have two possible values:  xy = -3\pi \approx -9.45  and  xy = \pi \approx 3.14 . Since both values are greater than -9.5, they both satisfy the condition in statement (2). Therefore, even with both statements, we cannot uniquely determine the value of  xy . Not sufficient.

Answer: E

Try NEW Algebra  PS question .

RonnieRon · Answer

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.

desaichinmay22 · Answer

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.

manpreetsingh86 · Answer

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

justbequiet · Answer

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

iliavko · Answer

Question, can someone show me the algebraic identity being used here, please? Is this a difference of squares?..

Bunuel · Answer

It's done by factoring quadratics or by solving quadratics for xy. Factoring Quadratics: https://www.purplemath.com/modules/factquad.htm Solving Quadratic Equations: https://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.

dineshril · Answer

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

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What is the value of xy?

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