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M30-22

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M30-22 [#permalink]

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New post 13 Oct 2014, 05:56
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A
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E

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  75% (hard)

Question Stats:

51% (01:17) correct 49% (01:43) wrong based on 47 sessions

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Re: M30-22 [#permalink]

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New post 13 Oct 2014, 07:47
Official 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: M30-22 [#permalink]

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New post 08 Jul 2015, 11:14
Bunuel

Can you tell me where am I wrong in the following:
From the sttmt A, we actually may get (xy-π)^2 - 4π^2=0. Then (xy-π)^2 = 4π^2. From then take the sqrt from both sides to arrive at a different solution from yours. Where did I go wrong?

Thank you in advance!
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Re: M30-22 [#permalink]

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New post 08 Jul 2015, 11:21
1
michaelyb wrote:
Bunuel

Can you tell me where am I wrong in the following:
From the sttmt A, we actually may get (xy-π)^2 - 4π^2=0. Then (xy-π)^2 = 4π^2. From then take the sqrt from both sides to arrive at a different solution from yours. Where did I go wrong?

Thank you in advance!

'
If you expand (xy-π)^2 - 4π^2=0 you'll get (xy)^2 - 2xyπ - 3π^2 = 0, which is not what we have i the firs statement (\(x^2y^2+2xy\pi-3\pi^2 = 0\)).
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Re: M30-22 [#permalink]

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New post 08 Jul 2015, 14:12
Bunuel wrote:
michaelyb wrote:
Bunuel

Can you tell me where am I wrong in the following:
From the sttmt A, we actually may get (xy-π)^2 - 4π^2=0. Then (xy-π)^2 = 4π^2. From then take the sqrt from both sides to arrive at a different solution from yours. Where did I go wrong?

Thank you in advance!

'
If you expand (xy-π)^2 - 4π^2=0 you'll get (xy)^2 - 2xyπ - 3π^2 = 0, which is not what we have i the firs statement (\(x^2y^2+2xy\pi-3\pi^2 = 0\)).


Ok, my mistake (pretty usual lately). How about (xy+π)^2 - 4π^2=0 ?
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Re: M30-22 [#permalink]

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New post 09 Jul 2015, 01:56
michaelyb wrote:
Bunuel wrote:
michaelyb wrote:
Bunuel

Can you tell me where am I wrong in the following:
From the sttmt A, we actually may get (xy-π)^2 - 4π^2=0. Then (xy-π)^2 = 4π^2. From then take the sqrt from both sides to arrive at a different solution from yours. Where did I go wrong?

Thank you in advance!

'
If you expand (xy-π)^2 - 4π^2=0 you'll get (xy)^2 - 2xyπ - 3π^2 = 0, which is not what we have i the firs statement (\(x^2y^2+2xy\pi-3\pi^2 = 0\)).


Ok, my mistake (pretty usual lately). How about (xy+π)^2 - 4π^2=0 ?


In this case you will get the same answer:

\((xy+\pi)^2=4\pi^2\).

\(xy+\pi=2\pi\) OR \(xy+\pi=-2\pi\).

\(xy=\pi\) OR \(xy=-3\pi\).

Hope it's clear.
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M30-22 [#permalink]

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New post 09 Jul 2015, 04:58
Actually, according to GMAT Club Math Book, the square root of an even number is always positive, so I thought that I cannot assume sqrt(4) = -2.
Please, see attached file "Square Root" - it´s a screenshot of the book.
>> !!!

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Re: M30-22 [#permalink]

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New post 30 Nov 2016, 09:45
Its not square root here..its square...and we can get square both from positive and negative value of a number....eg 25 can be obtained both from 5^2 & (-5)^2.
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Re M30-22 [#permalink]

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New post 23 Aug 2017, 07:58
1
I think this is a high-quality question and I agree with explanation.
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M30-22 [#permalink]

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New post 15 Feb 2018, 02:51
Hi Bunuel,

I'm completely lost as to how to factor out statement 1.

I did the following:

(xy)^2 + 2xy - 3pie^2 = 0
xy(xy + 2) - 3pie^2 = 0

I was then confused as to where to go next...I ended up guessing and picking C, but from this working, it appears that xy could be 3pie^2 or (-2) and combined with statement 2...would lead me to the correct answer of E.

However, according to your explanation the way I factored statement 1 was incorrect.

I've tried numerous times to factor out statement 1 the way you have but have had no luck thus far. How did you end up getting
(xy + 3pie) (xy - pie)

Thanks again.

Tosin
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Re: M30-22 [#permalink]

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New post 15 Feb 2018, 03:14
ttaiwo wrote:
Hi Bunuel,

I'm completely lost as to how to factor out statement 1.

I did the following:

(xy)^2 + 2xy - 3pie^2 = 0
xy(xy + 2) - 3pie^2 = 0

I was then confused as to where to go next...I ended up guessing and picking C, but from this working, it appears that xy could be 3pie^2 or (-2) and combined with statement 2...would lead me to the correct answer of E.

However, according to your explanation the way I factored statement 1 was incorrect.

I've tried numerous times to factor out statement 1 the way you have but have had no luck thus far. How did you end up getting
(xy + 3pie) (xy - pie)

Thanks again.

Tosin


Hope the links below help:

Factoring Quadratics
Solving Quadratic Equations
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M30-22 [#permalink]

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New post 06 May 2018, 09:03
1
Bunuel wrote:
What is the value of \(xy\)?



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

(2) \(xy>-9.5\)



Responding to a pm:

Put xy = z to make it easier to understand. It becomes just another quadratic

\(z^2 + 2z\pi - 3\pi^2 = 0\)
\(z^2 + 3z\pi - z\pi - 3\pi^2 = 0\)
\(z ( z + 3\pi) - \pi(z + 3\pi) = 0\)
\((z + 3\pi)*(z - \pi) = 0\)
\(z = \pi, -3\pi\)

Two values for xy. Not sufficient.

(2) \(xy>-9.5\)
Not sufficient alone

Using both, z can still be \(\pi\) or\(-3\pi\) ( which is -9.4 something).
Not sufficient.

Answer (E)

P. S. - Will respond to all PMs in the coming days (was travelling so was unable to get to the requests).
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Re: M30-22   [#permalink] 06 May 2018, 09:03
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