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If it is true that

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Carcass
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If it is true that [#permalink] New post   02 Aug 2021, 14:02
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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 abobe
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A
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motion2020
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If it is true that [#permalink] New post   02 Aug 2021, 16:19
\((m-3)(m+3)<0\) ---> (I) m<3 and m>-3, (II) m>3 and m<-3. Accept (I) and Reject (II)
m>-1 AND -3<m<3 ---> -1<m<3. Answer must be within (-1, 3). Answer is E
Options given
A. (-3, ∞)
B. (1, ∞)
C. (3, ∞)
D. (- ∞, 1)
E. Correct answer
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Re: If it is true that [#permalink] New post   03 Aug 2021, 05:03
hello expert, assist on this problem what do after talking square root on both side.
m<(+3)(-3)
-3<m<3. how to reach conclusion for option A.
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Re: If it is true that [#permalink] New post   03 Aug 2021, 05:52
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\(m < +-3\)

\(-3<m<3\)

\(m<-1\) is redundant Is there to trick you

Only A must be true

30 seconds approach
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Re: If it is true that [#permalink] New post   13 Aug 2021, 04:51
motion2020 wrote:
\((m-3)(m+3)<0\) ---> (I) m<3 and m>-3, (II) m>3 and m<-3. Accept (I) and Reject (II)
m>-1 AND -3<m<3 ---> -1<m<3. Answer must be within (-1, 3). Answer is E
Options given
A. (-3, ∞)
B. (1, ∞)
C. (3, ∞)
D. (- ∞, 1)
E. Correct answer



Sir, I am confused in this highlighted part. Would you mind helping me?
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If it is true that [#permalink] New post   Updated on: 13 Aug 2021, 09:54
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IMO answer must be E
COolguy101 wrote:
motion2020 wrote:
\((m-3)(m+3)<0\) ---> (I) m<3 and m>-3, (II) m>3 and m<-3. Accept (I) and Reject (II)
m>-1 AND -3<m<3 ---> -1<m<3. Answer must be within (-1, 3). Answer is E
Options given
A. (-3, ∞)
B. (1, ∞)
C. (3, ∞)
D. (- ∞, 1)
E. Correct answer



Sir, I am confused in this highlighted part. Would you mind helping me?

Originally posted by motion2020 on 13 Aug 2021, 05:24.
Last edited by motion2020 on 13 Aug 2021, 09:54, edited 1 time in total.
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Re: If it is true that [#permalink] New post   13 Aug 2021, 05:28
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motion2020 wrote:
IMO answer must be E
COolguy101 wrote:
motion2020 wrote:
\((m-3)(m+3)<0\) ---> (I) m<3 and m>-3, (II) m>3 and m<-3. Accept (I) and Reject (II)
m>-1 AND -3<m<3 ---> -1<m<3. Answer must be within (-1, 3). Answer is E
Options given
A. (-3, ∞)
B. (1, ∞)
C. (3, ∞)
D. (- ∞, 1)
E. Correct answer



Sir, I am confused in this highlighted part. Would you mind helping me?



Thank you very much sir for your swift response.
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Re: If it is true that [#permalink] New post   13 Aug 2021, 05:48
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The answer is A cannot be E
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If it is true that [#permalink] New post   13 Aug 2021, 06:23
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Carcass wrote:
The answer is A cannot be E

if answer is A and \(m>-3\) must be true, then \(m^2<9\) must not be true, for all cases of \(m>-3\)
\(m>-3\) implies all values of m to the right of the negative 3
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Re: If it is true that [#permalink] New post   13 Aug 2021, 08:36
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-3<m<3

Thi sis a must be true question and not could

C is m>3 so it is out immediately

B is m > 1 but we do know that m could be also 0 so is a could be true

D is m<1 and could be true but rules out the possibility to take into account values such as 2

A is m >-3 cover all our entire range.

My reasoning is that :)
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Re: If it is true that [#permalink] New post   13 Aug 2021, 08:47
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Carcass wrote:
\(m < +-3\)

\(-3<m<3\)

\(m<-1\) is redundant Is there to trick you

Only A must be true

30 seconds approach

If we select option A which is m > -3 then it also counts the possibility of m being equal to 3 or any other integer greater than that. Then this would contradict the statement mentioned in the question (i.e. m^2 < 9).
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If it is true that [#permalink] New post   13 Aug 2021, 08:55
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koala wrote:
Carcass wrote:
\(m < +-3\)

\(-3<m<3\)

\(m<-1\) is redundant Is there to trick you

Only A must be true

30 seconds approach

If we select option A which is m > -3 then it also counts the possibility of m being equal to 3 or any other integer greater than that. Then this would contradict the statement mentioned in the question (i.e. m^2 < 9).


That's is also true. clever observation. from -3 to infinite

However, the meaning of the question is : which one among the answer choices is " amust be true" regardless

:)
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Re: If it is true that [#permalink] New post   13 Aug 2021, 09:07
\(m^2<9\) and \(m>-1\) imply \(-3<m<3\) and \(m>-1\). This is only possible, if one takes on both intervals.

answer A \(m>-3\) is true for \(m>-1\), and it's true on the interval \(-3<m<3\), but it's not true for the interval as defined in the answer choice A itself \(m>-3\). It must be true implies true at all times.


Carcass 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 abobe
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Re: If it is true that [#permalink] New post   13 Aug 2021, 09:13
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ok ok guys

sorry. It is not the end.

It is just a discussion around a question :)


Simple is that
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Re: If it is true that [#permalink] New post   13 Aug 2021, 09:18
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Hi,

\(m^2<9\) & \(m>-1\)

So,
\(-3<m<3\) & \(m>-1\)

When we combine both these inequalities, we will get

\(-1 < m < 3\)

So in every case \(m\) will be greater than \(-3\)

Hence, answer A

motion2020 wrote:
\(m^2<9\) and \(m>-1\) imply \(-3<m<3\) and \(m>-1\). This is only possible, if one takes on both intervals.

answer A \(m>-3\) is true for \(m>-1\), and it's true on the interval \(-3<m<3\), but it's not true for the interval as defined in the answer choice A itself \(m>-3\). It must be true implies true at all times.
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Re: If it is true that [#permalink] New post   13 Aug 2021, 09:26
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:lol: :D Here we go. Join the army
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If it is true that [#permalink] New post   13 Aug 2021, 09:48
IF it is true that -1<m<3, THEN which of the following must be true

A. m>−3, IF A is FALSE, THEN m is not greater than -3. A is NOT FALSE, because m is greater than -3

B. m>1, IF B is FALSE, THEN m is not greater than 1. B is FALSE, because m can be -0.5 or 0; m is not greater than 1.

C. m>3, IF C is FALSE, THEN m is not greater than 3. C is FALSE, because m cannot be 3 and it's not greater than 3.

D. m<1, IF D is FALSE, THEN m is not less than 1. D is FALSE, because m can be 2 or 2.5; m is not less than 1.

E. ..

this is called proof by contradiction, and answer is indeed A
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Re: If it is true that [#permalink] New post   13 Aug 2021, 09:59
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motion2020 wrote:
IF it is true that -1<m<3, THEN which of the following must be true

A. m>−3, IF A is FALSE, THEN m is not greater than -3. A is NOT FALSE, because m is greater than -3

B. m>1, IF B is FALSE, THEN m is not greater than 1. B is FALSE, because m can be -0.5 or 0; m is not greater than 1.

C. m>3, IF C is FALSE, THEN m is not greater than 3. C is FALSE, because m cannot be 3 and it's not greater than 3.

D. m<1, IF D is FALSE, THEN m is not less than 1. D is FALSE, because m can be 2 or 2.5; m is not less than 1.

E. ..

this is called proof by contradiction, and answer is indeed A



sorry if I am wrong but the post with the paper attached was not E...minutes ago ??? :-o
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Re: If it is true that [#permalink] New post   13 Aug 2021, 10:19
It was repeated from the above solution lol. I managed to check If/Then statement for this question. Thanks for your original post. This question is quite didactic ☺️ another vocab entry popes out of my mind
Carcass wrote:
motion2020 wrote:
IF it is true that -1<m<3, THEN which of the following must be true

A. m>−3, IF A is FALSE, THEN m is not greater than -3. A is NOT FALSE, because m is greater than -3

B. m>1, IF B is FALSE, THEN m is not greater than 1. B is FALSE, because m can be -0.5 or 0; m is not greater than 1.

C. m>3, IF C is FALSE, THEN m is not greater than 3. C is FALSE, because m cannot be 3 and it's not greater than 3.

D. m<1, IF D is FALSE, THEN m is not less than 1. D is FALSE, because m can be 2 or 2.5; m is not less than 1.

E. ..

this is called proof by contradiction, and answer is indeed A



sorry if I am wrong but the post with the paper attached was not E...minutes ago ??? :-o


Posted from my mobile device
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Re: If it is true that [#permalink] New post   11 Apr 2022, 22:36
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m^2 < 9
divided by 3 ==> m < 3
divided by (-3) ==> m > -3
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