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# Is n < 0 ?

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Intern
Joined: 24 Feb 2013
Posts: 2
Is n < 0 ?  [#permalink]

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Updated on: 06 May 2014, 01:12
3
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:56) correct 35% (00:49) wrong based on 204 sessions

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Is n < 0 ?

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

My answer says, it would be C, although some expert says it will be E.

Originally posted by nayasnayas on 05 May 2014, 20:29.
Last edited by Bunuel on 06 May 2014, 01:12, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: Is n < 0 ?  [#permalink]

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06 May 2014, 01:20
nayasnayas wrote:
Is n < 0 ?

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

My answer says, it would be C, although some expert says it will be E.

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.

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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Posts: 2
Re: a small doubt  [#permalink]

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06 May 2014, 03:48
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
Intern
Joined: 19 Apr 2015
Posts: 13
Re: Is n < 0 ?  [#permalink]

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17 Nov 2015, 05:01
Bunuel wrote:
nayasnayas wrote:
Is n < 0 ?

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

My answer says, it would be C, although some expert says it will be E.

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.

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
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: Is n < 0 ?  [#permalink]

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17 Nov 2015, 08:52
aby0007 wrote:
Bunuel wrote:
nayasnayas wrote:
Is n < 0 ?

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

My answer says, it would be C, although some expert says it will be E.

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.

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)...
_________________
Intern
Joined: 19 Apr 2015
Posts: 13
Re: Is n < 0 ?  [#permalink]

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17 Nov 2015, 09:54
1
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.

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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Joined: 21 Aug 2013
Posts: 1429
Location: India
Re: Is n < 0 ?  [#permalink]

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19 Oct 2017, 00:39
(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
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Posts: 9419
Re: Is n < 0 ?  [#permalink]

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20 Nov 2018, 09:41
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Re: Is n < 0 ? &nbs [#permalink] 20 Nov 2018, 09:41
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# Is n < 0 ?

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