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GMAT Diagnostic Test Question 41

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GMAT Diagnostic Test Question 41 [#permalink] New post 29 Sep 2013, 20:57
Expert's post
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (02:24) correct 42% (03:46) wrong based on 151 sessions

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. -\frac{1}{64}
B. -\frac{1}{16}
C. -15
D. -16
E. -64
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Oct 2013, 23:29, edited 1 time in total.
Edited the question.
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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 29 Sep 2013, 20:58
Expert's post
Since one of the roots of the equation x^2 + ax + 15 = 0 is 3, then substituting we'll get: 3^3+3a+15=0. Solving for a gives a=-8.

Substitute a=-8 in the first equation: x^2-8x-b=0.

Now, we know that it has equal roots thus its discriminant must equal to zero: d=(-8)^2+4b=0. Solving for b gives b=-16.

Answer: D

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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 07 Oct 2013, 23:19
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bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650


The equation x^2 + ax + 15 = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. \frac{-1}{64}
B. \frac{-1}{16}
C. -15
D. -16
E. -64


Somethings is missing here. Question is "What is the value of b?" but 'b' is not present in the given data.
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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 07 Oct 2013, 23:29
Expert's post
Phoenix22 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650


The equation x^2 + ax + 15 = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. \frac{-1}{64}
B. \frac{-1}{16}
C. -15
D. -16
E. -64


Somethings is missing here. Question is "What is the value of b?" but 'b' is not present in the given data.


Edited the question. Thank you.

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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 25 Oct 2013, 06:58
The PDF has option D switched with Option B on this Page.
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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 16 Dec 2013, 03:51
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. -\frac{1}{64}
B. -\frac{1}{16}
C. -15
D. -16
E. -64



thanks for useful simple algebra example but could you explain what does mean has equal roots, please?
:wink:

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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 16 Dec 2013, 03:57
3111987 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. -\frac{1}{64}
B. -\frac{1}{16}
C. -15
D. -16
E. -64



thanks for useful simple algebra example but could you explain what does mean has equal roots, please?
:wink:


or this just means equation has only one solution( one root)?
many thanks :wink:

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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 16 Dec 2013, 04:01
Expert's post
3111987 wrote:
3111987 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0is 3. What is the value of b?

A. -\frac{1}{64}
B. -\frac{1}{16}
C. -15
D. -16
E. -64



thanks for useful simple algebra example but could you explain what does mean has equal roots, please?
:wink:


or this just means equation has only one solution( one root)?
many thanks :wink:


Yes, it means that the equation has one root.

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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 41 [#permalink] New post 06 Jan 2014, 01:19
bb wrote:
Since one of the roots of the equation x^2 + ax + 15 = 0 is 3, then substituting we'll get: 3^3+3a+15=0. Solving for a gives a=-8.

Substitute a=-8 in the first equation: x^2-8x-b=0.

Now, we know that it has equal roots thus its discriminant must equal to zero: d=(-8)^2+4b=0. Solving for b gives b=-16.

Answer: D


could you please explain the highlighted text. I don't understand what "discriminant" means. :oops:
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Re: GMAT Diagnostic Test Question 41 [#permalink] New post 06 Jan 2014, 02:28
Expert's post
khushboobhatia wrote:
bb wrote:
Since one of the roots of the equation x^2 + ax + 15 = 0 is 3, then substituting we'll get: 3^3+3a+15=0. Solving for a gives a=-8.

Substitute a=-8 in the first equation: x^2-8x-b=0.

Now, we know that it has equal roots thus its discriminant must equal to zero: d=(-8)^2+4b=0. Solving for b gives b=-16.

Answer: D


could you please explain the highlighted text. I don't understand what "discriminant" means. :oops:


You should brush up fundamentals.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

Hope this 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 41 [#permalink] New post 27 Mar 2014, 10:32
The PDF still notes that option D is the correct answer while B is noted as correct on this page, which is a result of the choices being flip-flopped.

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Re: GMAT Diagnostic Test Question 41   [#permalink] 27 Mar 2014, 10:32
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