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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] New post  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


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

Answer: C.

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] New post  11 Jun 2013, 02:10
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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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Re: If m<0, which of the following must be true? [#permalink] New post  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] New post  12 Jun 2013, 17:34
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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.

Answer: C.

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] New post  12 Jun 2013, 23:11
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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.

Answer: C.

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] New post  13 Aug 2014, 10:32
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goodyear2013 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


Apply the same logic as we used for this question.

All we know is that m is some negative number. We can see that C must be true: if m is negative then it MUST be true that it's less than 1.

Answer: C.
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Re: If m<0, which of the following must be true? [#permalink] New post  29 Aug 2014, 12:08
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In addition to Bunuel's reply

It helps to ask the question ( keeping in mind m is negative)
Will all negative numbers lie in the range 100<m<0 --No
Will all negative numbers <=-1 -- No
Will all negative numbers <= 1 -- Yes
Will all negative numbers lie between -100 and 100 -- No
For all negative numbers will m^2 >= 1/4 -- No
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Re: If m<0, which of the following must be true? [#permalink] New post  30 Aug 2014, 12:54
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What an odd problem. It's basically testing to see if you think that we know something about the absolute value of m (we don't). I suppose this gets tricky if you interpret the question as "Which of these could be the range of possible values of m?" because then B, D, & E all look good, and C looks impossible. Once you realize that m doesn't have to fit every value in the range, the problem becomes much easier. It's kind of like saying that if someone is younger than 18, they must also be younger than 100. Definitely true . . .
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Re: If m<0, which of the following must be true? [#permalink] New post  05 Sep 2014, 08:05
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Bunuel why not answer B?

Bunuel wrote:
goodyear2013 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


Apply the same logic as we used for this question.

All we know is that m is some negative number. We can see that C must be true: if m is negative then it MUST be true that it's less than 1.

Answer: C.
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If m<0, which of the following must be true? [#permalink] New post  05 Sep 2014, 08:06
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arindamsur wrote:
Bunuel why not answer B?

Bunuel wrote:
goodyear2013 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


Apply the same logic as we used for this question.

All we know is that m is some negative number. We can see that C must be true: if m is negative then it MUST be true that it's less than 1.

Answer: C.


Because if m is a number between -1 and 0, then B won't be true.
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Re: If m<0, which of the following must be true? [#permalink] New post  18 Apr 2015, 08:23
m <= 1
doesnt it mean m=1 at one point then m is not less than 0
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Re: If m<0, which of the following must be true? [#permalink] New post  18 Apr 2015, 11:58
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Hi sayansarkar,

This question is worded in a 'quirky' way. We're looking for an answer that will ALWAYS be true given the limitations that we have.

The prompt tells us just one thing about M.....M < 0, so M is negative.

The question asks which of the following MUST be true. By definition, EVERY negative number is less than or equal to 1. Technically-speaking, any positive number can be substituted in for "1" and this statement will still ALWAYS be true.

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Re: If m<0, which of the following must be true? [#permalink] New post  25 Apr 2015, 00:45
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I think some of you are assuming that m is an integer. As Bunuel pointed out, if m is between 0 and -1 (say, -1/2), then B will not be true. However, no matter what negative value we assign to m, it will always be less than 1. C would be correct even if it said "m ≤ 1,000,000." Yep, all negative numbers are less than 1,000,000. :)
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Re: If m<0, which of the following must be true? [#permalink] New post  08 May 2015, 00:38
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DmitryFarber wrote:
I think some of you are assuming that m is an integer. As Bunuel pointed out, if m is between 0 and -1 (say, -1/2), then B will not be true. However, no matter what negative value we assign to m, it will always be less than 1. C would be correct even if it said "m ≤ 1,000,000." Yep, all negative numbers are less than 1,000,000. :)


I am not able to understand...I considered integers too..
what if m=.5(m<=1) then m has to be negative and .5 is not negative.
please help!
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Re: If m<0, which of the following must be true? [#permalink] New post  08 May 2015, 00:50
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Careful, ssriva2, you are reasoning backwards. The fact here is that m<0, so it is definitely negative. Can m be .5? No. But must it be less than 1? Yes! All negative numbers are less than one, even though not all numbers less than one are negative.

Consider an analogy: I am shorter than the Eiffel Tower. Am I shorter than Mount Everest? Yes, of course! True, there are things shorter than Everest that are taller than the Eiffel Tower, but based on the facts provided, I am not one of them! :)
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Re: If m<0, which of the following must be true? [#permalink] New post  22 Feb 2017, 00:34
Bunuel wrote:
goodyear2013 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


Apply the same logic as we used for this question.

All we know is that m is some negative number. We can see that C must be true: if m is negative then it MUST be true that it's less than 1.

Answer: C.


Because of m is a number between -1 and 0, then B won't be true.[/quote]
Hi Bunuel,
Question stem says:
m<0, that means m is always negative. So, how do you consider '''m is a number between -1 and 0'''?
Thank you...
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If m<0, which of the following must be true? [#permalink] New post  22 Feb 2017, 01:12
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iMyself wrote:
Hi Bunuel,
Question stem says:
m<0, that means m is always negative. So, how do you consider '''m is a number between -1 and 0'''?
Thank you...


Because IF m is a number between -1 and 0, then B won't be true.

This is a response to a post asking why is not B an answer.
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Re: If m<0, which of the following must be true? [#permalink] New post  22 Feb 2017, 01:27
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iMyself wrote:
C says:
m ≤ 1, that means m is less than 1 up to negative infinity (i.e., m may be -100000). If m is a number between -1 and 0, then how C satisfy the question stem?
Thank you Bunuel for your nice help...


C is correct because we are given that m<0 (m is negative) and since m is negative then no matter what it is it's for sure ≤ 1.

Now, that particular response was as to why B is not correct. IF m is a number between -1 and 0, then B, which says that m is less than -1, won't be true.
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Re: If m<0, which of the following must be true? [#permalink] New post  22 Feb 2017, 04:37
Bunuel wrote:
iMyself wrote:
C says:
m ≤ 1, that means m is less than 1 up to negative infinity (i.e., m may be -100000). If m is a number between -1 and 0, then how C satisfy the question stem?
Thank you Bunuel for your nice help...


C is correct because we are given that m<0 (m is negative) and since m is negative then no matter what it is it's for sure ≤ 1.

Now, that particular response was as to why B is not correct. IF m is a number between -1 and 0, then B, which says that m is less than -1, won't be true.

Thanks with +2 kudos. Yes, I got it Bunuel finally. It's simple but tricky :). Can you say what difficulty level it may carry? just curiosity.
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Re: If m<0, which of the following must be true? [#permalink]
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