If m ≠ 0 and n ≠ 0, is mn 0?

Question

If m ≠ 0 and n ≠ 0, is mn > 0?

(1) |m + n| = k
(2) |m| + |n| = k

chetan2u · Answer

WHAT does the Q asks us? -- is mn>0? 
mn will be >0 ONLY if both m and n are of SAME sign- both positive or both negative.

lets check the statements-

(1) |m + n| = k 
We cannot say anything except that k is NOT negative
Insuff

(2) |m| + |n| = k 
same as statement I
Insuff

combined 
  we can say |m+n|=|m|+|n|..
this is possible ONLY if both m and n are of SAME sign.. 
|m|+|n| will always be SUM of numeric value of m and n..
But |m+n|will depend on the numeric value as also the sign..
If both are different signs, it will become a lesser numeric value.. 
say m= 4 and n=-5..
|m|+|n| = 4+5=9.. BUT |m+n|=|4-5|=1..
so both m and n are of same sign and hence mn>0..
Suff

deabas · Answer

|m+n| = |m| + |n| if and only if both m and n are positive numbers
--> E

chetan2u · Answer

Hi,

|m+n| = |m| + |n| even if both m and n are NEGATIVE numbers..
example let m =-4 and n = -7...
|m+n| = |-4-7| = |-11| =11..
|m|+|n| = |-4|+|-7| = 4+7 = 11..
so |m+n| = |m| + |n|

deabas · Answer

You are right chetan2u.. it was a silly mistake made by me... thank you for the correction.

shashankism · Answer

Given : m ≠ 0 and n ≠ 0 DS : mn > 0 which means wither m>0 and n>0 OR m<0 and n<0 Statement 1: |m + n| = k We can't say anything about m and n . m>0 or m<0 AND n>0 or n<0 NOT SUFFICIENT Statement 2: |m| + |n| = k We can't say anything about m and n . m>0 or m<0 AND n>0 or n<0 NOT SUFFICIENT Combined : Both |m + n| = k & |m| + |n| = k So, either both m>0 and n>0 OR m<0 and n<0. SUFFICIENT Answer C

ManishKM1 · Answer

Hi  chetan2u ,
 C  was apparent but I fell in the trap that Bunuel won't give such a straight forward Q. Can you pls guide me where is the mistake in B.

|m|+|n|=K
Sq both sides & expanding we get 2|m||n|=K^2-(m^2-n^2)
or |m||n|>=0, hence both m & n should be of the same sign????!!!

Thanks

If m ≠ 0 and n ≠ 0, is mn > 0?

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