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If ab=0, is |a-b|>0?

tagged by: VJesus12

Top Member

If ab=0, is |a-b|>0?

If ab=0, is |a-b|>0?

1) a=0
2) b<0

The OA is the option B.

Experts can you tell me why is not sufficient the statement (1)? I don't understand. I think the correct option is D.

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VJesus12 wrote:
If ab=0, is |a-b|>0?

1) a=0
2) b<0

The OA is the option B.

Experts can you tell me why is not sufficient the statement (1)? I don't understand. I think the correct option is D.
If ab = 0, then we have three states of the world:

1. a = 0, b doesn't equal 0
2. a doesn't equal zero, b = 0
3. a = 0, b = 0

For |a-b|>0 we need to be in state 1 or 2.

(1) doesn't tell which state of the world I am in, I know a = 0, but I don't know what b is - not sufficient
(2) b < 0 tells me I'm in state 1 and hence, |a-b|>0 (I can't be in any other state of the world and don't need to told the value for a because I know it is zero) - sufficient

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VJesus12 wrote:
If ab=0, is |a-b|>0?

1) a=0
2) b<0

The OA is the option B.

Experts can you tell me why is not sufficient the statement (1)? I don't understand. I think the correct option is D.
If ab=0 i.e. atleast one of the two variables is ZERO

Question: Is |a-b|>0?

Which is possible only if a ≠ b

i.e. Question: Is a = b ?

Statement 1: 1) a=0
we have no information about b and hence we can not compare whether a =b or a≠b hence
NOT SUFFICIENT

Statement 2: 2) b<0

b os negative
but one of the two variables a and b is definitely zero cause a*b = 0

hence, we can conclude that a≠b hence

SUFFICIENT

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