debayan222 wrote:
If m<0, which of the following must be true?
A. –100 < m < 100
B. m ≤ –1
C. m ≤ 1
D. m^2 ≥ 1/4
E. –100 < m < 0
P.S: Bunuel/VeritasPrepKarishma- guys I would request you to provide an explanation on this question.Also, please let me know whether it's a 700+ problem or not?
Folks-please come up with your explanations at the same time.
Since m is a negative number, then it must be less than 1.
Answer: C.
Other options:
A. –100 < m < 100 --> if m=-1,000, then this option is not true.
B. m ≤ –1 --> if m=-1/2, then this option is not true.
D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.
E. –100 < m < 0 --> if m=-1,000, then this option is not true.
P.S. I don't think that it's a 700+ question, more like 600.
The only reason I did not select option C was because it says "m ≤ 1 " which also includes a possibility of m=1 but when the question states that m=0 how can this be valid? Is it that we have selected option C because the possible values of m would be a sub set of the larger set (m ≤ 1 ) ?