bigfernhead wrote:

X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1

X>-1

|X|<1

|X|=1

|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.

after reading through all the posts, i finally got it. The answer is B because of the unique way the question is asked. I will categorize this as a "must be true" question.

I will not go into the details of solving the inequality. But the solution is -1<X<0 and X>1.

Now, let us consider a simpler question first. Assuming that John has more than 3 apples, which of the following statement MUST BE TRUE?

A) John has more than 5 apples

B) John has more than 2 apples

the answer is clearly B. The reason is that if John has more than 3 apples, thus he MUST have more than 2 apples.

A is wrong because it may not be true in all circumstances (e.g. John has 4 apples)

Going back to our question, we need to first solve the inequality to get -1<X<0 and X>1. Then, based on the solutions, we can transform the question into a simpler form:

assuming that -1<X<0 and X>1, which of the following statement MUST BE TRUE?

A) X>1

B) X>-1

Answer is B. The reason is that if the value of X is either -1<X<0 or X>1, then the value of X must be greater than X>-1.

A is wrong because it may not be true in all circumstances (e.g. X=-0.5)

Hope this helps