Does |r+s|=|m+n|?

Question

Does |r+s|=|m+n|?

(1) r+s=−m−n
(2) r=n+m−s

chetan2u · Answer

Hi,

First few MOD concept that are related here-
 1) Ofcourse any MOD is a +ive value..
2) any of the four cases would mean |a|=|b|
a=b ; a=-b ; -a=-b ; -a = b..
Because would convert any -ive value to positive

what does Q ask us ?
 Is the numeric value of r+s and m+n SAME? -- ONLY numeric value, irrespective of SIGN.. 
Now you will see both statements are SUFF

lets see the statements- 
 (1) r+s=−m−n 
r+s=-(m+n)
so the NUMERIC value of r+s and m+n is SAME, although the signs are different..
The MOD will change the -ive sign to +ive
Suff

(2) r=n+m−s 
r+s=m+n..
\Clearly suff

D
ans D

rahulkashyap · Answer

Alright could u please help explain the solution for this question?
Thank you

Lazybum · Answer

bumping this question, why do both statements not need to be true in order for the stem to be true?

there's 2 scenarios in the stem and unless both are true, how can we prove sufficiency?

chetan2u · Answer

If you have a=-b....this means |a|=|b|
Also if a=b, then |a|=|b|

Here too |r+s|=|m+n| means the same

r+s=m+n
OR
r+s=-(m+n)
Any of the above two if known will give our answer as YES since both lead to same answer and that is |r+s|=|m+n|

bumpbot · Answer

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Does |r+s|=|m+n|?

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