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

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If m<0, which of the following must be true? [#permalink]  10 Jun 2013, 19:50
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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?
[Reveal] Spoiler: OA

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Re: If m<0, which of the following must be true? [#permalink]  10 Jun 2013, 23:48
Expert's post
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?

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]  11 Jun 2013, 01:10
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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Correct me If I'm wrong !! looking for valuable inputs

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Joined: 27 Aug 2012
Posts: 1179
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Kudos [?]: 976 [0], given: 133

Re: If m<0, which of the following must be true? [#permalink]  11 Jun 2013, 01:13
Expert's post
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?

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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Re: If m<0, which of the following must be true? [#permalink]  11 Jun 2013, 05:35
Expert's post
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]  11 Jun 2013, 05:35
Expert's post
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?

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]  12 Jun 2013, 16:34
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?

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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Re: If m<0, which of the following must be true? [#permalink]  12 Jun 2013, 22:11
Expert's post
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?

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]  21 Jun 2014, 08:14
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