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Math Expert V
Joined: 02 Sep 2009
Posts: 60657
If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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Question Stats: 82% (01:22) correct 18% (02:10) wrong based on 617 sessions

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 60657
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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SOLUTION

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 $$b=-\frac{1}{2}$$.

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 60657
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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1
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 $$b=-\frac{1}{2}$$.

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

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Given $$b\neq{3}$$ , means $$b-3\neq{0}$$

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

$$b = \frac{-1}{2}$$

Intern  Joined: 30 Jan 2013
Posts: 6
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 $$b \neq {3}$$, then b=

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

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?

Originally posted by sabrina3509 on 27 Jun 2016, 16:24.
Last edited by Vyshak on 27 Jun 2016, 18:25, edited 1 time in total.
Formatting
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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1
(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

Math Expert V
Joined: 02 Sep 2009
Posts: 60657
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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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

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.
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Location: Hungary
Schools: Erasmus '19
GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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1
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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Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9145
Location: United States (CA)
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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Bunuel wrote:
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

We have:

b - 3 = 0

b = 3

Or

4 + 2/b = 0

2/b = -4

2 = -4b

-1/2 = b

Since b ≠ 3, then b must be -1/2.

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Joined: 03 Jun 2019
Posts: 1945
Location: India
GMAT 1: 690 Q50 V34 Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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Bunuel wrote:
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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Thank you!

Given:
1. (b-3)(4+2/b) = 0
2. b#3

If $$b \neq 0$$
4+2/b = 0
2/b = -4
b = -2/4 = -1/2 = -0.5

IMO C
SVP  D
Joined: 03 Jun 2019
Posts: 1945
Location: India
GMAT 1: 690 Q50 V34 Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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1
Bunuel wrote:
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Bunuel
b#3 should be replaced with
$$b \neq 3$$
Math Expert V
Joined: 02 Sep 2009
Posts: 60657
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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Kinshook wrote:
Bunuel wrote:
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Bunuel
b#3 should be replaced with
$$b \neq 3$$

__________________
Done. Thank you.
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Intern  B
Joined: 02 Apr 2019
Posts: 2
Location: India
GMAT 1: 640 Q48 V28
Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=  [#permalink]

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This was an easy one. The only thing one needed to pay attention to was b not equal to zero and 3 Re: If (b-3)(4+2/b) = 0 and b ≠ 3, then b=   [#permalink] 15 Sep 2019, 04:33
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