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

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If (a-1)(b-2) =0, which of the following must be true ? [#permalink] New post 21 Mar 2012, 13:52
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Question Stats:

64% (01:26) correct 36% (00:38) wrong based on 36 sessions
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, 14:02, edited 1 time in total.
Edited the question
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Re: PT #13 PS 4 Q 16 [#permalink] New post 21 Mar 2012, 13:57
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

So the answer is b)

If A doesnt equal 1, then b must equal 2
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Re: PT #13 PS 4 Q 16 [#permalink] New post 21 Mar 2012, 14:01
Expert's post
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


QUESTION SHOULD READ:

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.

Answer: B.
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Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink] New post 23 Mar 2012, 03:26
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.
Re: If (a-1)(b-2) =0, which of the following must be true ?   [#permalink] 23 Mar 2012, 03:26
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