If m

Question

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.

Bunuel · Accepted Answer

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.

Bunuel · Answer

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

Manhnip · Answer

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 ?

sps1604 · Answer

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 ) ? :?:

Bunuel · Answer

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.

Bunuel · Answer

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.

ankitaprsd · Answer

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

DmitryFarberMPrep · Answer

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 . . .

arindamsur · Answer

Bunuel why not answer B?

Bunuel · Answer

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

sayansarkar · Answer

m <= 1
doesnt it mean m=1 at one point then m is not less than 0

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

DmitryFarberMPrep · Answer

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.

ssriva2 · Answer

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!

DmitryFarberMPrep · Answer

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!

TheUltimateWinner · Answer

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

Bunuel · Answer

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.

Bunuel · Answer

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.

TheUltimateWinner · Answer

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.

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

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GMAT Problem Solving (PS) Questions

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

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