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.
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Is mn < 0?
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GMATinsight
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Question : Is mn<0?M7MBA wrote: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.
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
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Vincen
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Hello M7MBA.M7MBA wrote: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.
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.
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ErikaPrepScholar
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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.
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.
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