So, in statement 1, the answer would be yes if, say origin lied
somewhere here,
let's call it case 1, and the answer would be no, if origin
lied, let's say somewhere here,
let's call it case 2. So see, in both the cases, origin is
closer to c than it is to a. But in this case, 1, it lies
between a and c, in this case, 2, it lies,
it does not lie between a and c,
so 1 is not sufficient.
Let's come to statement 2. Distance between c and a is same
as this distance between c and -b.
So, one possibility is that b and -b and a coincide
that is when b is positive and this case, the origin would
be exactly between a and b.
So, this is case 3 and the answer in this case becomes yes.
However, the other possibility is when b itself is negative.
In that case, -b becomes positive and it comes somewhere
here. The distance between a and c,
this distance is same as this distance.
In this case, when b is here, -b comes here, let's call
it -b',  in this case,
the origin will be exactly between b and -b', the origin
will be, let's say, (somewhere) will be somewhere here.
This is case 4. So again, in case 4, the answer would be
no, in this case,
the answer would be yes.
So again, yes and no both are possible.
So, statement 2 is also not sufficient.
Now when we combine, when we combine in the  second
case, there were two possible values of -b: one was this value
and the other was this value.
But in this case, when -b comes here, the origin comes here,
origin becomes closer to a. But, statement 1 says the distance
of a from 0 is greater than, so origin cannot be closer to
a, and therefore, this possibility has to be eliminated and
therefore, this possibility has to exist and therefore, this
4th case is the only case that remains.
Okay and in 4th case, the answer
 becomes no. To reach to this
no - no, remember is also an answer, it's a unique answer, consistent
answer - to reach to this no, we had to use both the statements
and therefore, option C is the right choice.
