Number line

[itsme_sanket]

<-------r----s------t------------>

on the number line shown above, is zero half way between r and s ?


1) s is right to zero
2) the distance between t and r is same as distance between t and -s

Please provide explanations

[itsme_sanket]

any solu

[Dynamo]

IMO B

Statement 1

s is right to zero... speaks nothing of the position of r ... r can be right to zero too in that case zero will not be mid way...INSUFF

statement 2

if distance between t and r is same as the distance between t and -s then

r = -s

and between s and -s zero will always be mid way....

eg. 3 and -3......... SUFF

[Lhomme]

agree with dynamo. Has to be B. r and -s are the same. Hence 0 has to be midway from r and s.

[itsme_sanket]

i also marked it B ....but Official Answer is C..it is gmat prep question ...and i do not have explanation

[itsme_sanket]

Any posibilites of Official Answer as C ...@dynamo and @lhomme ?

[Dynamo]

Hmmmm

But what are your thoughts sanket... do you think we need to know the position of s once we know that r = -s???

[itsme_sanket]

no i donot think so we require A because

statement says
t + r = t -s ==> r + s = 0 ......so in case we have both values as opposite to each other in sign ....so i think it should suffice

May be i am missing something

[Lhomme]

answer has to be C

We do not know for sure that s is positive. We are assuming. What if s is negative. we can have all t r and s on the left side of 0. in that case -s is positive and will be on the right side of s. Hence we need to know both i) and ii) to know for siure that s is positive . Hence answer is C.

[Dynamo]

actually on second thoughts.... s can be -3 and then... everything changes...

if we do not know for sure that s is right of zero...

may be distance between t and r is same as distance between t and 3 or -s and it just expresses unit and nothing more.... so we cant assume that r=-s...

the answer should be C