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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:

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*:

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.