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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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madhavmarda
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If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   Updated on: 13 Sep 2014, 06:45
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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

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I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?
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Official Answer
A

Originally posted by madhavmarda on 12 Sep 2014, 22:41.
Last edited by Bunuel on 13 Sep 2014, 06:45, edited 1 time in total.
Renamed the topic and edited the question.
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Anamika2014
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If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   13 Sep 2014, 07:03
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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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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   13 Sep 2014, 06:55
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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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.
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If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   16 Nov 2014, 12:34
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


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.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   16 Nov 2014, 12:38
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kinjiGC wrote:
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


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.


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.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   16 Nov 2014, 22:47
since m^2>9
-3<m<3

given that m>-1

from both of these inequalities

m must be m>-3

Answer is A
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   23 May 2017, 05:39
Since m>-1
Hence m>-3

Smash that A.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   25 Dec 2017, 20:56
Expert Reply
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   03 Jan 2018, 14:27
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if m^2<9
= m^2-9<0
=(m-3)(m+3)<0
:- The roots are +3 and -3
so the range is -3<x<3 As per the Wavvy line method( don't get carried away by this Jargon just search for the keyword wavvy ,it is an easy concept of quadratic Inequlaity which you should be aware of )
and the range is also m>-1
combined together the intersection region in the number line is
-1<x<3 is the final range

Now Analyze each answer choices

(A) m > -3
The Option A is always correct, because for any number in the range -1<x<3 is always greater than -3

(B) m>1
The Option B is not always correct for any number in the range -1<x <3, because there are also numbers less than 1 in the range

(C) m>3
The Option C is always wrong because we have the range as -1<x <3

(D) m<1
The Option D is not always correct for any number in the range -1<x <3, because there are also numbers greater than 1 in the range


(E) None of the above


Answer is A
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   03 Jan 2018, 20:27
m^2<9 -> -3<m<3
AND m>-1
Therefore -1<m<3
m>-3 is true to all m that satisfies the above inequality.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   19 Nov 2018, 02:38
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


what if m= 4, it satisfies 1 but doesn't the equation in the question.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   19 Nov 2018, 03:06
Expert Reply
SauravSaket wrote:
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


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


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).
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   01 Jul 2021, 23:14
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


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
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   02 Jul 2021, 02:49
Expert Reply
Chitra657 wrote:
Bunuel wrote:
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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.


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


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.
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink] New post   31 Mar 2023, 03:33
Expert Reply
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

Show Spoiler
I believe the answer should be -1<m<3, however the answer key says m>-3.

Could someone explain this ?


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)
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Re: If it is true that m^2 < 9 and m > -1, which of the following must be [#permalink]
31 Mar 2023, 03:33
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