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This problem trains for: SAT-I, AMC-8, GMAT.

Let x, y, z, t, s, w be nonzero real numbers and consider their following combinations:

equation

equation

equation

Which of the following statements are false:

Obviously, none of the combinations can be zero, since none of the factors are zero. Therefore, III is true.

Also, by computing the product TSV:

equation

we see that in there are only even powers. Therefore, regardless of the signs of the numbers x, y, z, t, s, w, the product TSV is positive. If the three combinations would be simultaneously negative, the product TSV would be negative. Therefore, IV is also true.

The remaining statements are obviously false.