If it is true that m^2 -1, which of the following must be

Question

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 I believe the answer should be -1-3. Could someone explain this ?

Bunuel · Answer

m^2 < 9 means that -3 < m < 3. Combined with m > -1, we get that -1 < m < 3. Any m from this range must be greater than -3, hence A must be true.

Answer: A.

Anamika2014 · Answer

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.

kinjiGC · Answer

How m > -3 satisfy the must be true criteria.

Consider m = +4 does it satisfy? 
-1 < m < 3

Should be E) None of the above.

Bunuel · Answer

The correct answer is A, not E. You misinterpreted the question. We are given that that -1 < m < 3. If -1 < m < 3, then it must be true that m is greater than -3.

akumar5 · Answer

since m^2>9 -3-1 from both of these inequalities m must be m>-3 Answer is A

stonecold · Answer

Since m>-1
Hence m>-3

Smash that A.

Bunuel · Answer

Check other similar questions from  Trickiest Inequality Questions Type: Confusing Ranges  (part of our  Special Questions Directory ).

joepc · Answer

For Beginners if m^2<9 = m^2-9<0 =(m-3)(m+3)<0 :- The roots are +3 and -3 so the range is -3-1 combined together the intersection region in the number line is -1 -3 The Option A is always correct, because for any number in the range -11 The Option B is not always correct for any number in the range -13 The Option C is always wrong because we have the range as -1

Phuonganhtran · Answer

m^2<9 -> -3-1 Therefore -1-3 is true to all m that satisfies the above inequality.

SauravSaket · Answer

what if m= 4, it satisfies 1 but doesn't the equation in the question.

Bunuel · Answer

m cannot be 4 because m = 4 does not satisfy m^2 < 9. I suggest to check other similar questions from  Trickiest Inequality Questions Type: Confusing Ranges  (part of our  Special Questions Directory ).

Chitra657 · Answer

Bunuel 
m should be in the range of -1<m<3
so option A says m>-3
wont that include -2 as well?
I marked E as I thought it can include -2 as well which isnt right according to the inequality given in the question

Bunuel · Answer

Look at it this way: we are given that -1 < m < 3. ANY x from this range is for sure greater than -3. So, A is correct. Check the above discussion for more and links to similar questions.

Hope it helps.

KarishmaB · Answer

The question tests your understanding of "must be true" question types with some extraneous information added to confuse you.

We are given that m > -1 in all cases.

Then which of the following must be true? If m > -1 is all cases, then automatically, m will be greater than -3 in all cases too.
Say, m = 1 (which is greater than -1). Then of course, the value of 1 is greater than -3 too.

Answer (A)

satish_sahoo · Answer

So, the final set range of "m" if we can conclude will be:
-1<m<3

Now, for understanding, let's right the possible values of m= {-0.9, -0.8,...,0...1, 1.1, 1.2, ..., 1.9, 2}

Let's frame the answer options this way:
A) m>-3 ---> is asking are all the values of m greater than -3? Well YES!! This must be True.
B) m>1 ---> is asking are all the values of m greater than 1? No right? Coz if do have numbers less than 1 too.
C) m>3 ---> is asking are all the values of m greater than 3? No right? Coz all are actually less than 3.
D) m<1 ----> is asking are all the values of m lesser than 1? No right? Coz we have values of m greater than 1 too.
E) Can't be it, coz Opt A satisfies.

This is how i learned the ranges concept. If there's any flaw in my understanding please let me know.

P.S. We can draw a number line for visualization.

Thanks.

bumpbot · Answer

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If it is true that m^2 < 9 and m > -1, which of the following must be

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