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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.

Re: If (a-1)(b-2) =0, which of the following must be true ? [#permalink]
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]
03 Aug 2014, 19:43

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