madhavmarda wrote:
If it is true that \(m^2 < 9\) and \(m > -1\), which of the following must be true?
(A) m > -3
(B) m>1
(C) m>3
(D) m<1
(E) None of the above
The question tells us \(m^2 < 9\), which simplifies to \(-3 < m < 3\).
We are also told that \(m > -1\). Combining the two conditions we get, \(-1 < m < 3\).
Now the question asks, what
must be true. Let's look at the answer choices one at a time.
(A) \(m > -3\) ---- Since \(m > -1\), this will always be true. We have our answer and can stop right here. But let's look at the other answer choices just to be certain.
(B) \(m > 1\) ---- Not necessary. \(m\) can be \(0\).
(C) \(m > 3\) ---- False. \(m\) can never be more than \(3\).
(D) \(m < 1\) ---- Not necessary. \(m\) can be \(1\).
(E) None of the above ---- False, as we have already seen
A is true.
So, the answer is A.
Hope that helps.
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