Is mn < 0?

[M7MBA]

Is mn < 0? $$(1)\ \ \ m^5n^2<0$$ $$(2)\ \ \ m^{11}p^8n^5<0$$ The OA is the option B.

How can I know the sign of mn without knowing them? Experts, I would appreciate your help here.

[GMATinsight]

Is mn < 0? $$(1)\ \ \ m^5n^2<0$$ $$(2)\ \ \ m^{11}p^8n^5<0$$ The OA is the option B.

How can I know the sign of mn without knowing them? Experts, I would appreciate your help here.

Question : Is mn<0?

Statement 1: m^5n^2<0

but n^2 is always positive for any non zero value of n hence
m^5 is Negative
i.e. m <0 but the sign of n is unknown hence
NOT SUFFICIENT

Statement 2: m^11*p^8*n^5<0
p^8 is always positive for any non zero value of p hence
m^11 * n*5 < 0

For odd powers the sign doesn't change

Hence, mn<0
SUFFICIENT

Answer: option B

[Vincen]

Is mn < 0? $$(1)\ \ \ m^5n^2<0$$ $$(2)\ \ \ m^{11}p^8n^5<0$$ The OA is the option B.

How can I know the sign of mn without knowing them? Experts, I would appreciate your help here.

Hello M7MBA.

Here is how I solved it.

$$(1)\ \ \ m^5n^2<0$$ implies that m^5<0 and then m<0. But, we don't know anything about n. Therefore this statement is NOT SUFFICIENT.

$$(2)\ \ \ m^{11}p^8n^5<0$$ Now, we can rewrite the given expression as follows: $$m^{11}p^8n^5=mn\left(m^{10}p^8n^4\right)=mn\left(m^5p^4n^2\right)^2<0\ \Rightarrow\ \ mn<0\ \ \Rightarrow\ SUFFICIENT.$$ In conclusion, the correct answer is the option B. I hope it helps.

[ErikaPrepScholar]

Raising any positive or negative number to an even power will yield a positive number. Raising a negative number to an odd power will yield a negative number.

Statement 1
$$m^5n^2<0$$ n^2 must be positive whether n is positive or negative. This means that for the whole expression to be negative, m^5 must be negative. This tells us that m is negative. However, we do not know whether n is positive or negative. Insufficient.

Statement 2
$$m^11p^8n^5<0$$ p^8 must be positive whether p is positive or negative. This means that for the whole expression to be negative, either m^11 or n^5 must be negative, but the other must be positive. This means that either m or n must be negative, but the other must be positive. This means that mn must be negative. Sufficient.