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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
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (01:09) correct 45% (01:49) wrong based on 40 sessions

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Re: M30-22 [#permalink]

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New post 13 Oct 2014, 07:47
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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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New post 08 Jul 2015, 11:21
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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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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.


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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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124217 [0], given: 12076

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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
I think this is a high-quality question and I agree with explanation.

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Re M30-22   [#permalink] 23 Aug 2017, 07:58
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