gmatgrl wrote:
Is |x-1| < 1 ?
(1) (x-1)^2 >1
(2) x < 0
I don't know the official answer to this. But can someone help with the solution.
Even if you aren't sure how to do the algebra, this is a good DS problem for case testing. That's because the numbers involved are pretty simple, and there's only a single variable. It's always possible, when testing cases, that you'll miss something - but it's also the best way to prove that a statement is
insufficient, and it's better than just guessing or giving up because the algebra is complex.
(1)
Test extremes here. Start with a large number: x = 1000 fits the statement, since (1000-1)^2 is much greater than 1. Then, answer the question. Is |1000-1| < 1? No. It's greater.
Next, think about what you'd have to achieve to get a
different answer, in this case, a yes. You'd need a much smaller value of x. The smallest positive value of x that could possibly fit the statement would be something like 2.0001. But that also gives a 'no' answer, since |2.0001-1| is still greater than 1.
Try a negative value, as well. x = -0.5 works. But again, |-0.5-1| is greater than 1, so the answer is 'no'.
If you always get a 'no', the statement is sufficient.
(2)
Same situation - test a couple of negative values of x and notice that you always get a 'no', so it's sufficient. It's nice, but not always necessary, to logically reason out why you're always getting the same answer. But if the problem is tough and you're short on time, it's okay to just notice that every case seems to give the same result and decide that the statement is sufficient.
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