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Is n < 0 ? (1) m < n (2) -n < m

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nayasnayas
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Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   Updated on: 17 Apr 2022, 02:04
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Is n < 0 ?

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

Originally posted by nayasnayas on 05 May 2014, 21:29.
Last edited by Bunuel on 17 Apr 2022, 02:04, edited 3 times in total.
Renamed the topic and edited the question.
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Bunuel
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Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   06 May 2014, 02:20
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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.
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amanvermagmat
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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] 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
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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   16 Apr 2022, 11:40
Can someone please clear the statement 2 with taking the numerical values of n and m .
-n<m . Why it is not sufficient?

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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   17 Apr 2022, 02:09
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ArunGour wrote:
Can someone please clear the statement 2 with taking the numerical values of n and m .
-n<m . Why it is not sufficient?

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We know nothing about m, so -n < m gives us absolutely NO info about n. We just know that -n is less than some unknown number. How can we say anything about n from that?
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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   17 Apr 2022, 03:03
If we take n=0, then also both the condition are satisfied.
Can someone please explain, why it is not E.

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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   17 Apr 2022, 14:53
GauravAlugh wrote:
If we take n=0, then also both the condition are satisfied.
Can someone please explain, why it is not E.

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(1) m < n --> Implies m is to left of n on the number line. But we don't know whether n is +ve or -ve.
(2) -n < m --> Implies m + n > 0. But n can be -ve, +ve or zero.

Taking both statements together, implies m is to left of n on number line and their sum is +ve.
If n = 0, then as per statement 1, m has to be -ve and then the sum (m+n) cannot be > zero (i.e., Statement 2 fails).
Also, if n is -ve, then m is -ve and the sum (m+n) will be -ve (i.e., Statement 2 fails).

Hence, to make both statements true we need to have n +ve, giving a definitive answer 'NO' to the question 'Is n<0?'.
Hence, both statements together are sufficient.
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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink] New post   06 Jun 2022, 05:06
My 2 cents on this:

is n<0?

S1: m<n

m-n<0 which doesn't tell us anything. m=? n=?

S2: -n<m

Same issue. Don't know either n or m and hence cannot answer. Insufficient.

S1 and S2 together.

Remember, inequalities of same direction (sign) can be added.

n>m from S1 and we rewrite -n<m and n>-m from S2

Adding both statements:

n>m
n>-m
---------

2n > 0
n>0 ----> Definitive Answer.

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Re: Is n < 0 ? (1) m < n (2) -n < m [#permalink]
06 Jun 2022, 05:06
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Bunuel
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