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Re: If abc 0. Is abc > 0 ? (1) |a b | = |a| - |b| (2) |b + c| = |b|
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21 Mar 2023, 15:27
From the question stem...
We know that none of a, b or c can be zero.
The question is asking us for the combination of negative and positive values from the variables. For instance, if a and b are negative, but c is positive, abc will be positive.
Statement 1: |a–b|=|a|−|b|
From absolute value properties, we know that this can only be true if |a| > |b| and if a and b are the same sign OR if b = 0 (which we know from the question stem cannot be the case). We know the signs for a and b are the same, but we don't know what sign c is, which could change the sign of abc (e.g. if a and b are negative, c can be positive or negative and we would have two different answers). Not sufficient (eliminate A and D).
Statement 2: |b+c|=|b|+|c|
Again, from absolute value properties, this can only be true if b and c are the same sign. Similar to the rationale above, we don't know what sign a is, which could change the sign of abc. Not sufficient (eliminate B).
Statement 1 and 2
The statements combined tell us that a, b and c are all the same sign. However, the two scenarios (all negative and all positive) produce two different results!
Even with both statements, the information provided is not sufficient.
Answer is E.