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# If ab - 2b = (4 - a)b, what is the value of b?

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Joined: 28 Aug 2016
Posts: 17
GMAT 1: 560 Q44 V23
If ab - 2b = (4 - a)b, what is the value of b?  [#permalink]

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Updated on: 12 Jan 2017, 22:40
9
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Difficulty:

95% (hard)

Question Stats:

42% (02:11) correct 58% (02:15) wrong based on 83 sessions

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If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

Originally posted by Amby02 on 12 Jan 2017, 22:21.
Last edited by Bunuel on 12 Jan 2017, 22:40, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 7958
If ab - 2b = (4 - a)b, what is the value of b?  [#permalink]

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13 Jan 2017, 22:45
amberbajaj02 wrote:
If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

Hi..
Equation is ab-2b=(4-a)b..... ab-2b=4b-ab.....2ab-6b=0
2b(a-3)=0...
So two relations
1) if a=3, b can be 0 or anything else.
2)if $$a\neq{3}$$, b has to be 0..

Let's see the statements

(1) |a^2 - 9| ≤ 0
LHS has to be 0 as MOD cannot be NEGATIVE..
So a^2-9=0.... a can be 3 or -3..
If a is 3, ans bcan be anything..
If a is -3, b is 0..
Insufficient

(2) a < 0
This means $$a\neq{3}$$.
So b is 0..
Sufficient

B
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Re: If ab - 2b = (4 - a)b, what is the value of b?  [#permalink]

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14 Jan 2017, 08:01
It is better to first solve the equation to see what information is already given:

ab - 2b = (4 - a)b
ab - 2b = 4b -ab
2ab = 6b

ab = 3b (Notice - do not cancel out b from both the sides here, because b can be zero). - Consider this one of the GMAT's trap, which is used in many questions.

ab - 3b = 0

b (a-3) = 0

Either b = 0 or a = 3

now a stmt would be sufficient if it tells that $$a\neq{3}$$ because in that case we will say "b (a-3) = 0" is true because b = 0.

(1) |$$a^2$$ - 9| ≤ 0
a mod is never negative hence $$a^2 - 9$$ = 0 i.e. a is 3 or -3
insufficient - because if a =3 then we do not know whether b = 0 or not but if a = -3 then certainly b = 0.

(2) a < 0
if a is negative then $$a\neq{3}$$. hence b=0
sufficient.
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Re: If ab - 2b = (4 - a)b, what is the value of b?  [#permalink]

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26 Sep 2019, 06:35
Amby02 wrote:
If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

$$ab-2b=(4-a)b…ab-2b=4b-ab…2ab=6b…2ab-6b=0…2b(a-3)=0$$
[i] $$2b=0,…(a-3)=anything$$
[ii] $$(a-3)=0…a=3,…2b=anything$$

(1) $$|a^2 - 9| ≤ 0…LHS≥0…|a^2 - 9|=0…a=(3,-3)$$: insufic.
if $$a=3,…b=anything$$; if $$a=-3,…b=0$$

(2) a < 0: [ii] case is not valid, so [i] $$2b=0,…(a-3)=anything$$, sufic.

Re: If ab - 2b = (4 - a)b, what is the value of b?   [#permalink] 26 Sep 2019, 06:35
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