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nayasnayas
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Bunuel
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amanvermagmat
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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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Bunuel
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ArunGour
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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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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GauravAlugh
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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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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