On a certain number line, conditions are a<b<c<d<e and abcd>0. Which of the following must be true?
I ab>0 II cd>0 III de>0 ,IV e+ve
=ve  Select the correct option.
A) I only
B) II only
C) III only
D) I and II only
E) I II and IV
Givena<b<c<d<e abcde="" and="">0.   Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.   We are given : I ab&gt;0 II cd&gt;0 III de&gt;0   case 1: a and b can be negative/positive and if they are... we get greater than 0.   case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0.   case 2: we have de , then c and d both can be negative/positive and if they are... we get greater than 0.   if cd both negative , then de both have to negative in order to get greater than 0. In order to abcde&gt;0 , cde can't be negative else we get -ve value, then we need to have either a or b as negative then ab can't be greater than 0.   so cde have to be positive.   ab &gt; 0 , cd &gt; 0 obviouly e will be positive , since we have information de&gt; 0 . ( Here we have relationship between cd and de , where d is common).   So cases 1 and 2 are fine.   OptionI II and IV</b<c<d<e>
<result>E</result>
On a certain number line, conditions are a<b<c<d<e and abcd>0. Which of the following must be true?
I ab>0 II cd>0 III de>0 ,IV e+ve
=ve