bagdbmba 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.
One way to tackle this question (s) is to think in terms of necessary condition. Must be true is something that necessarily hold true.
So if we negate an answer choice, then the prompt must also be negated.
In the choices above let us go one by one-
1) negate A==> m < -100 . This will lead to affirm the prompt. or m> 100 . This will lead to rejecting the prompt. We want only a no/rejection answer.
2) reject B ==> m> -1 . This again leads to both acceptance m = -1/2 or rejection m = 5.
3) reject c == m> 1 . This only leads to rejection ..if m > 1 then no way can we have m <0. So this is our answer!
4) m is not equal to 1/2 and m is not equal to 1/2. again we can have positive and negative values. Affirmation and rejection are both possible
5) rejecting E, it is easy to see why it will also lead to rejection or affirmation.
Hope this helps