study wrote:

Bunuel, the expert, is there a better way to solve this problem. I just took the Prep test and took me a long time to test each number. Is theer a quicker way to do this?

This is a hard problem. Below is another way of solving it:

On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?The distance between x and y is greater than the distance between x and z, means that we can have one of the following four scenarios:

A.

y--------z--x (YES case)

B.

x--z--------y (YES case)

C.

y--------x--z (NO case)

D.

z--x--------y (NO case)

The question asks whether we have scenarios A or B (z lie between x and y ).

(1) xyz <0 --> either all three are negative

or any two are positive and the third one is negative. We can place zero between y and z in case A (making y negative and x, z positive), then the answer would be YES

or we can place zero between y and x in case C, then the answer would be NO. Not sufficient.

(2) xy<0 --> x and y have opposite signs. The same here: We can place zero between y and x in case A, then the answer would be YES

or we can place zero between y and x in case C, then the answer would be NO. Not sufficient.

(1)+(2) Cases A (answer YES) and case C (answer NO) both work even if we take both statement together, so insufficient.

A.

y----0----z--x (YES case) --> xyz<0 and xy<0;

C.

y----0----x--z (NO case) --> xyz<0 and xy<0

Answer: E.

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