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Manager  Joined: 31 Oct 2011
Posts: 213
If (a-1)(b-2) =0, which of the following must be true ?  [#permalink]

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14 00:00

Difficulty:   25% (medium)

Question Stats: 63% (00:47) correct 37% (01:00) wrong based on 402 sessions

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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

Originally posted by eybrj2 on 21 Mar 2012, 14:52.
Last edited by Bunuel on 21 Mar 2012, 15:02, edited 1 time in total.
Edited the question
Manager  B
Joined: 22 Feb 2012
Posts: 84
Schools: HBS '16
GMAT 1: 740 Q49 V42 GMAT 2: 670 Q42 V40 GPA: 3.47
WE: Corporate Finance (Aerospace and Defense)
Re: PT #13 PS 4 Q 16  [#permalink]

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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

So the answer is b)

If A doesnt equal 1, then b must equal 2
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: PT #13 PS 4 Q 16  [#permalink]

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2
1
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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Manager  Joined: 07 Dec 2011
Posts: 71
Location: India
Re: If (a-1)(b-2) =0, which of the following must be true ?  [#permalink]

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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.
Manager  Joined: 11 Jun 2014
Posts: 54
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45 WE: Information Technology (Consulting)
Re: If (a-1)(b-2) =0, which of the following must be true ?  [#permalink]

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(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.
Intern  Joined: 03 Aug 2014
Posts: 6
Concentration: Operations, Healthcare
GMAT 1: 730 Q48 V42 WE: Operations (Pharmaceuticals and Biotech)
Re: If (a-1)(b-2) =0, which of the following must be true ?  [#permalink]

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

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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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If (a-1)(b-2) =0, which of the following must be true ?   [#permalink] 13 Jun 2019, 09:45
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