Heres a question that I think is incorrectly explained.

If x is not equal to 0, is |x| less than 1?

(1) x / |x| < x

(2) |x| > x

The explaination given in the answers is below

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The question "Is |x| less than 1?" can be rephrased in the following way.

Case 1: If x > 0, then |x| = x. For instance, |5| = 5. So, if x > 0, then the question becomes "Is x less than 1?"

Case 2: If x < 0, then |x| = -x. For instance, |-5| = -(-5) = 5. So, if x < 0, then the question becomes "Is -x less than 1?" This can be written as follows:

-x < 1?

or, by multiplying both sides by -1, we get

x > -1?

Putting these two cases together, we get the fully rephrased question:

"Is -1 < x < 1 (and x not equal to 0)"?

Another way to achieve this rephrasing is to interpret absolute value as distance from zero on the number line. Asking "Is |x| less than 1?" can then be reinterpreted as "Is x less than 1 unit away from zero on the number line?" or "Is -1 < x < 1?" (The fact that x does not equal zero is given in the question stem.)

(1) INSUFFICIENT: If x > 0, this statement tells us that x > x/x or x > 1. If x < 0, this

statement tells us that x > x/-x or x > -1. This is not enough to tell us if -1 < x < 1.

(2) INSUFFICIENT: When x > 0, x > x which is not true (so x < 0). When x < 0, -x > x or

x < 0. Statement (2) simply tells us that x is negative. This is not enough to tell us if -1 < x < 1.

(1) AND (2) SUFFICIENT: If we know x < 0 (statement 2), we know that x > -1 (statement 1). This means that -1 < x < 0. This means that x is definitely between -1 and 1.

The correct answer is C.

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Look at the question carefully.

1. Tells us that x / |x| < x

or 1/|x| < 1

This will only hold if |x| > 0 or x E {-infinity,-1} U {1, infinity}. Eitherway, its sufficent to say that |x| > 1 which is what the question is asking

2. Tells us that |x| > x

This will only hold if x E {-infinity,0} and does no mean that |x| > 1.

eg |-0.25| = 0.25. If we assume x to be integers only (which the question does not state) then its sufficentl

In either case, (C) is incorrect. It should be A or D.

Your response ?