What is the value of xy?

Question

New project from GMAT Club: Topic-wise questions with tips and hints!

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the value of xy?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the value of xy?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards