Arithmetic Question

[gxklin]

If a, b, and c are nonzero integres, is a^5b^3c^4 negative?

1) b is negative
2) ac is negative.

I got C but the answer is E, can someone explain why?

This is a Y/N question; taken both statements together, the signs are either (-)(-)(+) or (+)(-)(-), with both ending in a positive number, so isn't this sufficient to say a^5b^3c^4 IS NOT negative?

Thanks

[RonPurewal]

This is a Y/N question; taken both statements together, the signs are either (-)(-)(+) or (+)(-)(-), with both ending in a positive number, so isn't this sufficient to say a^5b^3c^4 IS NOT negative?

nope. it appears that you are blithely ignoring the exponents in this problem -- i.e., your reasoning would be correct if the question just asked about abc, but it doesn't; it asks about (a^5)(b^3)(c^4).

in this case, then, c^4 is positive no matter what -- remember that raising either a negative or a positive number to an EVEN POWER produces a positive result -- so the issue is really just (a^5)(b^3).
that product is positive in your first case above, and negative in your second case above. hence, still insufficient.