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# If (a-1)(b-2) =0, which of the following must be true ?

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Senior Manager
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If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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21 Mar 2012, 14:52
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If (a-1)(b-2) =0, which of the following must be true ?

I. a=1 and b=2
II. if a is not = 1, then b=2
III. if a=1, then b is not=2

A. I only
B. II only
C. III only
D. I and II
E. II and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2012, 15:02, edited 1 time in total.
Edited the question

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Math Expert
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Re: PT #13 PS 4 Q 16 [#permalink]

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21 Mar 2012, 15:01
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eybrj2 wrote:
If (a - 1) (b - 1) = 0, which of the following must be true?

1. a = 1 and b = 2

2. If a is not 1, then b = 2

3. If a =1, then b is not 2.

a) 1 only

b) 2 only

c) 3 only

d) 1 and 2

e) 2 and 3

If (a-1)(b-2) =0, which of the following must be true ?
I. a=1 and b=2
II. if a is not = 1, then b=2
III. if a=1, then b is not=2

A. I only
B. II only
C. III only
D. I and II
E. II and III

$$(a-1)(b-2) =0$$ --> either $$a=1$$ or $$b=2$$ (or both).

I. a=1 and b=2 --> not necessarily true: for example if a=1 then b can be any number
II. if a is not = 1, then b=2 --> if $$a\neq{1}$$ then in order $$(a-1)(b-2) =0$$ to hold true then $$b=2$$ MUST be true;
III. if a=1, then b is not=2 --> not necessarily true: $$a=1$$ and $$b=2$$ can be simultaneously true.

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Re: PT #13 PS 4 Q 16 [#permalink]

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21 Mar 2012, 14:57
You need to edit the question sir..

should be:

(a-1)(b-2)=0

The only thing you can say for sure is either a = 1 or b = 2 or both

If A doesnt equal 1, then b must equal 2

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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23 Mar 2012, 04:26
B. II only

I is not necessarily true as it makes both (a-1) and (b-2) equal zero which is not necessarily true. if either one of these were equal to zero it would satisfy the equation

II must be true. If a is not = 1 the (a-1)#0 there (b-2) must be equal to zero and b =2

III not necessarily true. It may be the case that a=1 and b=2 as this would lead to 0x0=0 which satisfies the equation.

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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03 Aug 2014, 20:43
Hello from the GMAT Club BumpBot!

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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03 Aug 2014, 21:30
(a-1)(b-2)=0
so either a=1 or b=2 or both. It 'or' not 'and', so it could be any of the three possibilities. so I and III cannot be always true.

so the answer is B, II only.

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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03 Aug 2014, 21:48
if (a-1)(b-2) =0 then one of the following have to be true:

1. a = 1, and b can be any number
2. b = 2, and a can be any number
3. both and a = 1, b = 2

hope this helps

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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13 Nov 2015, 06:22
Hello from the GMAT Club BumpBot!

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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]

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23 Nov 2016, 06:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If (a-1)(b-2) =0, which of the following must be true ?   [#permalink] 23 Nov 2016, 06:45
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