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Is n < 0 ?

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Is n < 0 ? [#permalink]

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New post 05 May 2014, 21:29
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Is n < 0 ?

(1) m < n
(2) -n < m

[Reveal] Spoiler:
My answer says, it would be C, although some expert says it will be E.

Could anyone please advice !

Thanks in advance. :)
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 May 2014, 02:12, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Is n < 0 ? [#permalink]

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New post 06 May 2014, 02:20
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nayasnayas wrote:
Is n < 0 ?

(1) m < n
(2) -n < m

[Reveal] Spoiler:
My answer says, it would be C, although some expert says it will be E.

Could anyone please advice !

Thanks in advance. :)


Is n < 0 ?

(1) m < n. n is greater than some number m. This is clearly insufficient to say whether n is negative. Not sufficient.

(2) -n < m --> 0 < m + n. The sum of n and some number m is positive. This is also insufficient to say whether n is negative. Not sufficient.

(1)+(2) We can sum the inequalities with the signs in the same direction: m + (-n) < n + m --> 2n > 0 --> n > 0. Sufficient.

Answer: C.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule 3. Thank you.
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Re: a small doubt [#permalink]

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New post 06 May 2014, 04:48
Even i feel answer should be C , as from a) n> m and from b) n>-m, if we combine both the statements n can never be negative. We can pick some values and check .
1. n and m are positive numbers :- n= 2 , m=1 here 2>1 and 2>-1 -> n is positive
2. n and m are negative numbers :- n = -1 , m = -2 here -1 > -2 and -1 > 2 (not possible ) -> n cannot be negative
3. n is positive or 0 and m is 0 or negative number :- n =1 , m = -1 here 1> -1 and 1 > 1 (not possible ) ; n=1 , m = 0 here 1>0 and 1>0 -> n is positive ; n=0 , m = -1 here 0 > -1 and 0 > 1(not possible )
4. n is negative and m is positive -> Not possible

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Re: Is n < 0 ? [#permalink]

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New post 17 Nov 2015, 06:01
Bunuel wrote:
nayasnayas wrote:
Is n < 0 ?

(1) m < n
(2) -n < m

[Reveal] Spoiler:
My answer says, it would be C, although some expert says it will be E.

Could anyone please advice !

Thanks in advance. :)


Is n < 0 ?

(1) m < n. n is greater than some number m. This is clearly insufficient to say whether n is negative. Not sufficient.

(2) -n < m --> 0 < m + n. The sum of n and some number m is positive. This is also insufficient to say whether n is negative. Not sufficient.

(1)+(2) We can sum the inequalities with the signs in the same direction: m + (-n) < n + m --> 2n > 0 --> n > 0. Sufficient.

Answer: C.



Hope it helps.






Hey Bunuel,

I totally understand the explanation, but have one doubt. If we put values in the equations my observation is coming out a little different please correct me where I am wrong.

1. m<n

m=2;
n=8;

2. -n<m

m=2;
n= -8;

Adding 1 and 2
we get -n<m<n;

or

-8<2<8;

So by just considering n as +ve value both conditions can be satisfied. Please correct me where I am wrong

Kudos [?]: 6 [0], given: 0

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Re: Is n < 0 ? [#permalink]

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New post 17 Nov 2015, 09:52
aby0007 wrote:
Bunuel wrote:
nayasnayas wrote:
Is n < 0 ?

(1) m < n
(2) -n < m

[Reveal] Spoiler:
My answer says, it would be C, although some expert says it will be E.

Could anyone please advice !

Thanks in advance. :)


Is n < 0 ?

(1) m < n. n is greater than some number m. This is clearly insufficient to say whether n is negative. Not sufficient.

(2) -n < m --> 0 < m + n. The sum of n and some number m is positive. This is also insufficient to say whether n is negative. Not sufficient.

(1)+(2) We can sum the inequalities with the signs in the same direction: m + (-n) < n + m --> 2n > 0 --> n > 0. Sufficient.

Answer: C.



Hope it helps.






Hey Bunuel,

I totally understand the explanation, but have one doubt. If we put values in the equations my observation is coming out a little different please correct me where I am wrong.

1. m<n

m=2;
n=8;

2. -n<m

m=2;
n= -8;

Adding 1 and 2
we get -n<m<n;

or

-8<2<8;

So by just considering n as +ve value both conditions can be satisfied. Please correct me where I am wrong


Sorry your question is not clear... Also, I guess you meant n = 8 not n = -8 on (2)...
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132827 [0], given: 12378

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Re: Is n < 0 ? [#permalink]

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New post 17 Nov 2015, 10:54
Is n < 0 ?

(1) m < n. n is greater than some number m. This is clearly insufficient to say whether n is negative. Not sufficient.

(2) -n < m --> 0 < m + n. The sum of n and some number m is positive. This is also insufficient to say whether n is negative. Not sufficient.

(1)+(2) We can sum the inequalities with the signs in the same direction: m + (-n) < n + m --> 2n > 0 --> n > 0. Sufficient.

Answer: C.



Hope it helps.






Hey Bunuel,

I totally understand the explanation, but have one doubt. If we put values in the equations my observation is coming out a little different please correct me where I am wrong.

1. m<n

m=2;
n=8;

2. -n<m

m=2;
n= -8;

Adding 1 and 2
we get -n<m<n;

or

-8<2<8;

So by just considering n as +ve value both conditions can be satisfied. Please correct me where I am wrong[/quote]

Sorry your question is not clear... Also, I guess you meant n = 8 not n = -8 on (2)...[/quote]


Hey Bunuel,

Never mind I got it now.

Thanks.

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Re: Is n < 0 ? [#permalink]

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New post 19 Oct 2017, 01:39
(1) m < n .. obviously not sufficient

(2) -n < m.. not sufficient but if we multiply both sides by -1 we get
n > -m

Combine the two statements: n is greater than both m and -m. So obviously 'n' can be neither 0 nor less than 0 (if n is zero it cannot be simultaneously greater than positive and negative of another number. If n is less than 0 then it will obviously be less than whichever out of m and -m is positive). So n is > 0. Sufficient to answer. So C answer

Kudos [?]: 160 [0], given: 270

Re: Is n < 0 ?   [#permalink] 19 Oct 2017, 01:39
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