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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, 19:50
Expert's post
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

44% (01:40) correct 55% (00:44) wrong based on 67 sessions
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] New post 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?
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, 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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Re: If m<0, which of the following must be true? [#permalink] New post 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?
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.



Bunuel,
Thanks for your reply.

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.

Appreciate your feedback.
_________________

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Re: If m<0, which of the following must be true? [#permalink] New post 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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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



Bunuel,
Thanks for your reply.

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.

Appreciate your feedback.


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

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

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

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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