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

Question

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

Bunuel · Accepted Answer

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
eq{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.

AbeinOhio · Answer

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

karun0109 · Answer

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.

sshrivats · Answer

(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.

vvLA · Answer

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

BlueRocketAsh · Answer

I. It is true when a=1 and b=2 but it is not a must. Only one term has to be zero.

II. One term must be zero. Therefore this statement is true

III. If a=1 b can be any number

Therefore only II is the essential requirement. Answer is B

bumpbot · Answer

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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 ?

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