On a certain number line, conditions are x<y<z<u<v and xyzuv>0. Which of the following must be true?
I xy>0 II zu>0 III zu>0  Choose the most appropriate option:	A) I only	B) I & II only	C) III only	D) II only	E) II and III only
Givenx<y<z<u<v and="" xyzuv="">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 xy&gt;0 II yz&gt;0 III uv&gt;0   case 1: x and y can be negative/positive and if they are... we get greater than 0.   case 2: we have zu , then z and u both can be negative/positive and if they are... we get greater than 0.   case 2: we have uv , then z and u both can be negative/positive and if they are... we get greater than 0.   if zu both negative , then de both have to negative in order to get greater than 0. In order to xyzuv&gt;0 , zuv can't be negative else we get -ve value, then we need to have either x or y as negative then ab can't be greater than 0.   so cde have to be positive.   xy &gt; 0 , yz &gt; 0 obviouly v will be positive , since we have information uv&gt; 0 . ( Here we have relationship between cd and uv , where u is common).   Option I &amp; II only.</y<z<u<v>
<result>B</result>
On a certain number line, conditions are x<y<z<u<v and xyzuv>0. Which of the following must be true?
I xy>0 II zu>0 III zu>0