dzodzo85 wrote:
If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?
(1) rt is negative
(2) s is negative
Could someone kindly render a more easily understood explanation than that found in the Quantitative Review 2nd Edition. It would be really appreciated.
Since r, s, and t are
nonzero integers then in order r^5*s^3*t^4 to be negative, only one condition should hold: r and s must have the opposite signs, in this case (r^5*s^3)*t^4=(negative)*(positive)=negative.
Notice that if we were not told that given variables are nonzero then there would be one more condition that t must not be zero.(1) rt is negative --> r and t have the opposite signs. Not sufficient, since no info about s.
(2) s is negative. Clearly insufficient.
(1)+(2) If r is positive then the answer will be YES (since r^5*s^3*t^4=positive*negative*positive=negative) but if r is negative then the answer will be NO (r^5*s^3*t^4=negative*negative*positive=positive). Not sufficient.
Answer: E.
Hope it helps.
For (1)+(2), how could R be positive? Isn't T automatically positive because it is T^4?
Statement 1 says RT is negative, so I assumed that R has to be negative. I'm sure this is an elementary question, but can you please show me an example of how T^4 could be negative?