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In the equation x^2 + bx + 12 = 0, x is a variable and b is

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In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink] New post 29 Jan 2014, 01:14
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
(2) 4 is a root of the equation x^2 + bx + 12 = 0.

Data Sufficiency
Question: 62
Category: Algebra First- and second-degree equations
Page: 157
Difficulty: 600


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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink] New post 29 Jan 2014, 01:15
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SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Answer: D.
_________________

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

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink] New post 29 Jan 2014, 01:51
From S1:x-3 is a factor of the given equation=>x=3 is a root of the equation.Putting x=3 in the eq x^2+bx+12 we can get the value of b.Hence sufficient.
From S2:4 is a root of the equation=>Putting x=4 in the equation we can find out b.Sufficient.
Ans.D
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink] New post 01 Feb 2014, 08:45
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SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Answer: D.
_________________

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.


What are GMAT Club Tests?
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is   [#permalink] 01 Feb 2014, 08:45
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