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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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23 Dec 2013, 07:42
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81% (01:09) correct 19% (01:44) wrong based on 604 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

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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23 Dec 2013, 07:44
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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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23 Dec 2013, 11:23
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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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24 Dec 2013, 03:36
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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 $$b=-\frac{1}{2}$$.

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

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11 Sep 2014, 02:52
Given $$b\neq{3}$$ , means $$b-3\neq{0}$$

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

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

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

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Updated on: 27 Jun 2016, 18:25
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.
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Re: If (b-3)(4+ 2/b) = 0 and not equal to 3, then b=  [#permalink]

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27 Jun 2016, 18:24
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

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

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27 Jun 2016, 21:50
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

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

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29 Apr 2017, 01:00
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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Re: If (b-3)(4+2/b) = 0 and b#3, then b=  [#permalink]

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27 Sep 2018, 17:37
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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Re: If (b-3)(4+2/b) = 0 and b#3, then b= &nbs [#permalink] 27 Sep 2018, 17:37
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