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If (b-3)(4+2/b) = 0 and b#3, then b=

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If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (b-3)(4+2/b) = 0 and b#3, then b=

(A) -8
(B) -2
(C) -1/2
(D) 1/2
(E) 2

Problem Solving
Question: 5
Category: Algebra Second-degree equations
Page: 62
Difficulty: 500


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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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If (b-3)(4+2/b) = 0 and b#3, then b=

(A) -8
(B) -2
(C) -1/2
(D) 1/2
(E) 2

\((b-3)(4+\frac{2}{b}) = 0\) means that \(b-3=0\) or \(4+\frac{2}{b}=0\). Since \(b\neq{3}\), then \(b-3\neq{0}\) and thus \(4+\frac{2}{b}=0\). From which it follows that \(b=-\frac{1}{2}\).

Answer: C.
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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

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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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Since b#3,this implies (4+2/b) = 0 and thus 4= - 2/b or b = -1/2

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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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If (b-3)(4+2/b) = 0 and b#3, then b=

(A) -8
(B) -2
(C) -1/2
(D) 1/2
(E) 2

\((b-3)(4+\frac{2}{b}) = 0\) means that \(b-3=0\) or \(4+\frac{2}{b}=0\). Since \(b\neq{3}\), then \(b-3\neq{0}\) and thus \(4+\frac{2}{b}=0\). From which it follows that \(b=-\frac{1}{2}\).

Answer: C.
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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

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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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New post 11 Sep 2014, 01:52
Given \(b\neq{3}\) , means \(b-3\neq{0}\)

So, \(4+\frac{2}{b} = 0\)

\(b = \frac{-1}{2}\)

Answer = C
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If (b-3)(4+ 2/b) = 0 and not equal to 3, then b= [#permalink]

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New post 27 Jun 2016, 15:24
If (b-3)(4+ 2/b) = 0 and \(b \neq {3}\), then b=

a) -8
b) -2
c)-1/2
d) 1/2
e) 2

[Reveal] Spoiler:
I got the solution through substituting the answers, but could someone show me how to reduce the factors to get rid of the fraction in the second factor? How do I solve it algebriacely?

Last edited by Vyshak on 27 Jun 2016, 17:25, edited 1 time in total.
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Re: If (b-3)(4+ 2/b) = 0 and not equal to 3, then b= [#permalink]

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New post 27 Jun 2016, 17:24
(b - 3)(4 + 2/b) = 0

b = 3 or 2/b = -4

Its given \(b \neq {3}\)

So, 2/b = -4 --> b = -2/4 = -1/2

Answer: C
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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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New post 27 Jun 2016, 20:50
sabrina3509 wrote:
If (b-3)(4+ 2/b) = 0 and \(b \neq {3}\), then b=

a) -8
b) -2
c)-1/2
d) 1/2
e) 2

[Reveal] Spoiler:
I got the solution through substituting the answers, but could someone show me how to reduce the factors to get rid of the fraction in the second factor? How do I solve it algebriacely?


Merging topics.

Please refer to the discussion above.
_________________

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

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Re: If (b-3)(4+2/b) = 0 and b#3, then b= [#permalink]

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New post 29 Apr 2017, 00:00
This is the Zero Product Property.

It says that, if:

a × b = 0 then a = 0 or b = 0 or both equal zero

So, in \(\left( b-3 \right) \left( 4+\cfrac { 2 }{ b } \right) =0\):

\(b-3=0\) and \(4+\cfrac { 2 }{ b } =0\)

Since \(b\neq 3\) then \(4+\cfrac { 2 }{ b } =0\rightarrow \left( 4+\cfrac { 2 }{ b } =0 \right) b\rightarrow 4b+2=0\rightarrow 4b=-2\rightarrow b=-\cfrac { 2 }{ 4 } \rightarrow b=-\cfrac { 1 }{ 2 }\)
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Re: If (b-3)(4+2/b) = 0 and b#3, then b=   [#permalink] 29 Apr 2017, 00:00
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