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# If m<0, which of the following must be true?

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BSchool Forum Moderator
Joined: 27 Aug 2012
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If m<0, which of the following must be true? [#permalink]

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10 Jun 2013, 20:50
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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.
[Reveal] Spoiler: OA

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Re: If m<0, which of the following must be true? [#permalink]

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11 Jun 2013, 00:48
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debayan222 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.

Since m is a negative number, then it must be less than 1.

Other options:

A. –100 < m < 100 --> if m=-1,000, then this option is not true.

B. m ≤ –1 --> if m=-1/2, then this option is not true.

D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.

E. –100 < m < 0 --> if m=-1,000, then this option is not true.

P.S. I don't think that it's a 700+ question, more like 600.
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Re: If m<0, which of the following must be true? [#permalink]

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11 Jun 2013, 02:10
Bunuel

In Option C it says "m less or equal to 1" than if m<0 given in the main condition how does it m<= 1 will always satisfy the condition,

I choose D in doubt as It said m<0 , so my thought process was $$m^2$$ will always be positive, but I was not sure if $$m^2 > 1/2$$

what should be the approach in these kind of problems ?
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Joined: 27 Aug 2012
Posts: 1193
Re: If m<0, which of the following must be true? [#permalink]

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11 Jun 2013, 02:13
Bunuel wrote:
debayan222 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.

Since m is a negative number, then it must be less than 1.

Other options:

A. –100 < m < 100 --> if m=-1,000, then this option is not true.

B. m ≤ –1 --> if m=-1/2, then this option is not true.

D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.

E. –100 < m < 0 --> if m=-1,000, then this option is not true.

P.S. I don't think that it's a 700+ question, more like 600.

Bunuel,

I've some doubts, hope you'll help me clarifying those...

Here, C appears as the best option. But, generally speaking, for 'must be true' questions I guess it should 'always be true'.If that's so, for m<1, m can be 0.5 and hence it violates the given condition m<0.

I guess I'm thinking in a wrong line and that's why need your clarification to find out where i'm going wrong.

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Posts: 39581
Re: If m<0, which of the following must be true? [#permalink]

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11 Jun 2013, 06:35
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Manhnip wrote:
Bunuel

In Option C it says "m less or equal to 1" than if m<0 given in the main condition how does it m<= 1 will always satisfy the condition,

I choose D in doubt as It said m<0 , so my thought process was $$m^2$$ will always be positive, but I was not sure if $$m^2 > 1/2$$

what should be the approach in these kind of problems ?

If m is a negative number, then it must be less less than 1.

Consider following:
If $$x=5$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If $$-1<x<10$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY $$x$$ from $$-1<x<10$$ will be less than 120 so it's always true about the number from this range to say that it's less than 120.
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Re: If m<0, which of the following must be true? [#permalink]

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11 Jun 2013, 06:35
debayan222 wrote:
Bunuel wrote:
debayan222 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.

Since m is a negative number, then it must be less than 1.

Other options:

A. –100 < m < 100 --> if m=-1,000, then this option is not true.

B. m ≤ –1 --> if m=-1/2, then this option is not true.

D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.

E. –100 < m < 0 --> if m=-1,000, then this option is not true.

P.S. I don't think that it's a 700+ question, more like 600.

Bunuel,

I've some doubts, hope you'll help me clarifying those...

Here, C appears as the best option. But, generally speaking, for 'must be true' questions I guess it should 'always be true'.If that's so, for m<1, m can be 0.5 and hence it violates the given condition m<0.

I guess I'm thinking in a wrong line and that's why need your clarification to find out where i'm going wrong.

Check here: if-m-0-which-of-the-following-must-be-true-154150.html#p1234728
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Re: If m<0, which of the following must be true? [#permalink]

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12 Jun 2013, 17:34
Bunuel wrote:
debayan222 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.

Since m is a negative number, then it must be less than 1.

Other options:

A. –100 < m < 100 --> if m=-1,000, then this option is not true.

B. m ≤ –1 --> if m=-1/2, then this option is not true.

D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.

E. –100 < m < 0 --> if m=-1,000, then this option is not true.

P.S. I don't think that it's a 700+ question, more like 600.

The only reason I did not select option C was because it says "m ≤ 1 " which also includes a possibility of m=1 but when the question states that m=0 how can this be valid? Is it that we have selected option C because the possible values of m would be a sub set of the larger set (m ≤ 1 ) ?
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Joined: 02 Sep 2009
Posts: 39581
Re: If m<0, which of the following must be true? [#permalink]

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12 Jun 2013, 23:11
sps1604 wrote:
Bunuel wrote:
debayan222 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.

Since m is a negative number, then it must be less than 1.

Other options:

A. –100 < m < 100 --> if m=-1,000, then this option is not true.

B. m ≤ –1 --> if m=-1/2, then this option is not true.

D. m^2 ≥ 1/4 (m≤-1/2 or m≥1/2) --> if m=-1/4, then this option is not true.

E. –100 < m < 0 --> if m=-1,000, then this option is not true.

P.S. I don't think that it's a 700+ question, more like 600.

The only reason I did not select option C was because it says "m ≤ 1 " which also includes a possibility of m=1 but when the question states that m=0 how can this be valid? Is it that we have selected option C because the possible values of m would be a sub set of the larger set (m ≤ 1 ) ?

Yes, possible value of m (negative numbers) are a subset of the larger set (m ≤ 1 ).

Check here: if-m-0-which-of-the-following-must-be-true-154150.html#p1234728

Hope it helps.
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Re: If m<0, which of the following must be true? [#permalink]

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21 Jun 2014, 09:14
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Re: If m<0, which of the following must be true? [#permalink]

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03 Jun 2016, 07:30
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Re: If m<0, which of the following must be true? [#permalink]

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03 Jun 2016, 08:54
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.

IMO, all the options are wrong.

If option C were m<1 then it holds true, but the option is m<= 1. Since it is given that m<0, it can not be = 1

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Re: If m<0, which of the following must be true? [#permalink]

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19 Jun 2017, 21:20
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
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Re: If m<0, which of the following must be true? [#permalink]

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20 Jun 2017, 09:32
Precondition is m<0
The possible values of m would be a sub set of the larger set (m ≤ 1 ) which would also include values like 0.4,0.5,0.6.... etc which actually discards the initial condition.
For me it should be none of the options which is not listed in the answer set.
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Re: If m<0, which of the following must be true? [#permalink]

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20 Jun 2017, 09:36
FB2017 wrote:
Precondition is m<0
The possible values of m would be a sub set of the larger set (m ≤ 1 ) which would also include values like 0.4,0.5,0.6.... etc which actually discards the initial condition.
For me it should be none of the options which is not listed in the answer set.

This is explained several times above with different additional examples. Please read the whole thread before posting. Thank you.
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Re: If m<0, which of the following must be true? [#permalink]

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20 Jun 2017, 11:03
IMO C
Its a tricky question .
We can take as many numbers for other options , but only option C hols true for every value of m .
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Re: If m<0, which of the following must be true? [#permalink]

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20 Jun 2017, 19:17
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

We are given that m is a negative number and must determine which of the answer choices must be true. Scanning the answers, we see that the only answer that has to be true IN ALL CASES is m must be less than or equal to 1, since all negative numbers are less than or equal to 1.

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Re: If m<0, which of the following must be true?   [#permalink] 20 Jun 2017, 19:17
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# If m<0, which of the following must be true?

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