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GMAT Diagnostic Test Question 13

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GMAT Diagnostic Test Question 13 [#permalink] New post 06 Oct 2013, 23:12
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A
B
C
D
E

Difficulty:

  65% (medium)

Question Stats:

26% (02:41) correct 74% (01:17) wrong based on 264 sessions
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 06 Oct 2013, 23:14
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Explanation:
Official Answer: D.


If x=\sqrt[4]{x^3+6x^2}, then the sum of all possible solutions for x is:

A. -2
B. 0
C. 1
D. 3
E. 5

Take the given expression to the 4th power: x^4=x^3+6x^2;

Re-arrange and factor out x^2: x^2(x^2-x-6)=0;

Factorize: x^2(x-3)(x+2)=0;

So, the roots are x=0, x=3 and x=-2. But x cannot be negative as it equals to the even (4th) root of some expression (\sqrt{expression}\geq{0}), thus only two solution are valid x=0 and x=3.

The sum of all possible solutions for x is 0+3=3.

Answer: D.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 07 Oct 2013, 07:20
So, the roots are x=0, x=3 and x=-2. But x cannot be negative as it equals to the even (4th) root of some expression (\sqrt{expression}\geq{0}), thus only two solution are valid x=0 and x=3.

Why exactly is the even fourth root be negative.

Lets say we have a number 16 whose square root can be +- 4

Fourth roots can be +-2 -----> (-2) * (-2) * (-2) * (-2) = 16

Hence if \sqrt{expression} = \sqrt{16}

Why cant x= -2 ? We are selecting all -2 here

I might be wrong, but best to ask and clear any ambiguity.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 07 Oct 2013, 08:48
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irda wrote:
So, the roots are x=0, x=3 and x=-2. But x cannot be negative as it equals to the even (4th) root of some expression (\sqrt{expression}\geq{0}), thus only two solution are valid x=0 and x=3.

Why exactly is the even fourth root be negative.

Lets say we have a number 16 whose square root can be +- 4

Fourth roots can be +-2 -----> (-2) * (-2) * (-2) * (-2) = 16

Hence if \sqrt{expression} = \sqrt{16}

Why cant x= -2 ? We are selecting all -2 here

I might be wrong, but best to ask and clear any ambiguity.


When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. That is, \sqrt{25}=5, NOT +5 or -5.

In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Hope it helps.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: GMAT Diagnostic Test Question 13 [#permalink] New post 08 Jun 2014, 04:33
Bunuel wrote:
irda wrote:
So, the roots are x=0, x=3 and x=-2. But x cannot be negative as it equals to the even (4th) root of some expression (\sqrt{expression}\geq{0}), thus only two solution are valid x=0 and x=3.

Why exactly is the even fourth root be negative.

Lets say we have a number 16 whose square root can be +- 4

Fourth roots can be +-2 -----> (-2) * (-2) * (-2) * (-2) = 16

Hence if \sqrt{expression} = \sqrt{16}

Why cant x= -2 ? We are selecting all -2 here

I might be wrong, but best to ask and clear any ambiguity.


When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. That is, \sqrt{25}=5, NOT +5 or -5.

In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Hope it helps.



I would like to know if this is officially declared in GMAC's website- that GMAT only accepts +ve root. This is a clear ambiguity in terms of answer logic.
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Re: GMAT Diagnostic Test Question 13 [#permalink] New post 08 Jun 2014, 04:43
Expert's post
lakhyajd wrote:
Bunuel wrote:
irda wrote:
So, the roots are x=0, x=3 and x=-2. But x cannot be negative as it equals to the even (4th) root of some expression (\sqrt{expression}\geq{0}), thus only two solution are valid x=0 and x=3.

Why exactly is the even fourth root be negative.

Lets say we have a number 16 whose square root can be +- 4

Fourth roots can be +-2 -----> (-2) * (-2) * (-2) * (-2) = 16

Hence if \sqrt{expression} = \sqrt{16}

Why cant x= -2 ? We are selecting all -2 here

I might be wrong, but best to ask and clear any ambiguity.


When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. That is, \sqrt{25}=5, NOT +5 or -5.

In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Hope it helps.



I would like to know if this is officially declared in GMAC's website- that GMAT only accepts +ve root. This is a clear ambiguity in terms of answer logic.


Official Guide for GMAT® Review, 13th Edition:
\sqrt{n} denotes the positive number whose square is n. For example, \sqrt{9} denotes 3.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: GMAT Diagnostic Test Question 13   [#permalink] 08 Jun 2014, 04:43
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