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01 Aug 2022, 20:25
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Kimberly77
Our calculation shows that either c = 0 or a = 1. If c = 0, then the answer to the question is "0". If a = 1, then c need not be 0. We don't know the value of c when a = 1, but as long as c ≠ 0, it does not matter. In this case, the answer to the question is some number other than 0. Since we have two contradicting answers, statement one alone is not sufficient.
Notice that we cannot take c = 0, since c already has a predetermined value. We must determine whether we have enough information to determine the value of c. Since it is also possible that c ≠ 0, we cannot find a unique value for c, which is why this statement is not sufficient.
04 Aug 2022, 14:10
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Thanks ScottTargetTestPrep for the clarification and makes sense now.
Since it's very easy to mistaken c= 0 at this stage
a x c = c
ac - c = 0
c(a - 1) = 0
c = 0 or a = 1
So does it mean it's always good to verify both c=0 and a=1 value to see will it still satisfy a x c = c then right? As only then we know c=0 result can very depending on a ? Thanks
Since it's very easy to mistaken c= 0 at this stage
a x c = c
ac - c = 0
c(a - 1) = 0
c = 0 or a = 1
So does it mean it's always good to verify both c=0 and a=1 value to see will it still satisfy a x c = c then right? As only then we know c=0 result can very depending on a ? Thanks
04 Aug 2022, 20:04
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Kimberly77
You must always consider every possibility and check whether you can get contradicting answers to the question that you need to answer. For instance, in this problem, the question is "What is the value of c?". Our calculation gave us two possibilities, c = 0 and a = 1. We must check each of these possibilities and see whether we always get the same value for c or we get different values for c. When we check the possibility of c = 0, there is only one possible value of c, which is 0. When we check the possibility of a = 1, we see that there are more than one possible values for c (though we only need one value besides c = 0). For instance, we can let a = 1 and c = 5. Notice that a * c = c is satisfied for these values. So 5 is another possible value for c, and since the question "What is the value of c?" has more than one possible answer, this means that statement two alone is not sufficient.
It could happen both a = 1 and c = 0 result in the same value of c (for instance, if the equation were a * c = 0). If that were the case, then we would conclude that the statement was sufficient to answer the question.
