Oski wrote:
brokerbevo wrote:
Ahhh, I see what you mean in regard to the AND / OR in regard to my first question. Thanks.
;)
brokerbevo wrote:
As for my second question, I understand how the statements work, however, even if the statements can be used alone, they can not contradict each other because the statements are always true. So, as a rule of thumb, if the statements contradict each other, a math mistake was made. I'm not saying your answer is wrong, I'm just trying to understand the logic because inequalities is my biggest weakness. Thanks for your patience.
Logic: back to the basics :D
You have an answer (S) and 2 propositions (1) and (2).
Different GMAT answers are:
(A): (1) => (S) and (2) ≠> (S)
(B): (1) ≠> (S) and (2) => (S)
(C): (1) ≠> (S), (2) ≠> (S) and [ (1) & (2) ] => (S)
(D): (1) => (S) and (2) => S
(E): (1) ≠> (S), (2) ≠> (S) and [ (1) & (2) ] ≠> (S)
In particular for (D), it is not a matter of (1) & (2), you have to consider them separately.They are the hypotheses, and the question is "if you assume (1) is true, is (S) true or false or we don't know ?" and then a separate question is "if you assume (2) is true, is (S) true or false or we don't know ?"
A very simple illustration:
Imagine a GMAT question which would be: "(S) Is x>0?"
(1) x>2
(2) x<-1
Clearly, (1) and (2) are contradictory since you cannot have both x<-1 AND x>2, but that's not the point.
If (1) is true you can answer question (S) (if x>2 then x>0 is true)
If (2) is true you can answer question (S) (if x<-1 then x>0 is false)
So answer would be (D) as well, even if (1) and (2) are contradictory.
I hate to beat a dead horse (of course I don't of anyone who beats dead horses but nonetheless), I completely understand how the statements and the ABCDE choices work in a DS problem. All I am saying is that the statements can never contradict. The statements will nonetheless show different information, maybe even the same piece of information just stated in a different way, but they can never contradict each other. For example, if you have the following DS problem:
Q: is x = 4?
(1) x^2 = 16
(2) x < 0
And lets say your work was as followed:
(1) x = 4 SUFFICIENT to answer
(2) x is negative and thus x does not equal 4 SUFFICIENT to answer ----> since both statemenst are sufficient to answer, your answer would undoubtedly be D. However, when you take a step back and look at your work for each statement you would say "wait, how can x be 4 yet x also be a negative number?" Therefore, you know you made a math mistake somewhere. Now, of course, this is an ultra-simplified example, and of course statement (1) would be x = +/- 4 and the answer would be B, but it does hold the same logic in that the statement are always true. When problems get more complex, it might be a good idea to take a step back and ask yourself if your final outcomes of each statement contradict each other. The hard part is viewing the statements in isolation to determine whether statement (1) is enough information to answer the question or if statement (2) is enough to answer the question, if not, then you go on to C or E. This is a tip given by
MGMAT prep to double-check your work. I hope this helps. Anyway, thanks for the explanation of the inequalities, I added your answer and reasoning to my study sheet and I understand inequalities a lot more now. As I said, this is my biggest weakness. I wish everything in the world could be equal instead of inequal -- it would make the math a lot easier. Thanks.