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Is zero half way between S and R ?

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by ithamarsorek » Wed Feb 16, 2011 4:29 pm
1) I agree, not sufficient
2) I don't understand why it is insufficient.
Does S2 say that T-R=T-(-S) ===> T-R = T+S ====> R+S=0
Isn't this sufficient to know if zero is half way between S and R?


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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Feb 16, 2011 8:02 pm
Solution:
<-----r---------s--------t----->
We need to know whether (r+s)/2 = 0 or not?
Consider (1) alone.
It means that s>0, t>0.
Also r < s < t.
Obviously, (1) alone is not sufficient.
Next, consider (2) alone.
lt-rl =lt-(-s)l =lt+sl.
So, (t-r)^2 = (t+s)^2
Or t^2 - 2*t*r +r^2 = t^2 + 2*t*s + s^2.
Or (r+s)(r-s) - 2t(r+s) = 0.
Or (r+s)(r-s-2t) = 0.
Or either r = -s or r-s = 2t.
So If (2) holds, either r = -s or t = (r-s)/2.
If r = -s, then (r+s)/2 = 0.
But if t = (r-s)/2, it is not necessary that (r+s)/2 = 0.
Or (2) alone is not sufficient.
Next, consider both (1) and (2) combined.
r < s.
Or (r - s) < 0.
So, if we take t = (r-s)/2, we get that t < 0.
But this is contradictory since t > 0 according to (1).
So, the only possibility is r = -s or (r+s)/2 = 0.
Or 0 is halfway between r and s.
So, both statements together are sufficient.
The correct answer is (C).
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by ankur.agrawal » Thu Feb 17, 2011 12:42 am
Gr8 Solution Anurag.

Was trying to solve this through number line but cud net get a sure shot answer from that.

This algebraic approach is much more full proof.

But i am afraid whether i will be able to play around with algebra, if a different variety of question like these pops up in the exam.

:o(.
Anurag@Gurome wrote:Solution:
<-----r---------s--------t----->
We need to know whether (r+s)/2 = 0 or not?
Consider (1) alone.
It means that s>0, t>0.
Also r < s < t.
Obviously, (1) alone is not sufficient.
Next, consider (2) alone.
lt-rl =lt-(-s)l =lt+sl.
So, (t-r)^2 = (t+s)^2
Or t^2 - 2*t*r +r^2 = t^2 + 2*t*s + s^2.
Or (r+s)(r-s) - 2t(r+s) = 0.
Or (r+s)(r-s-2t) = 0.
Or either r = -s or r-s = 2t.
So If (2) holds, either r = -s or t = (r-s)/2.
If r = -s, then (r+s)/2 = 0.
But if t = (r-s)/2, it is not necessary that (r+s)/2 = 0.
Or (2) alone is not sufficient.
Next, consider both (1) and (2) combined.
r < s.
Or (r - s) < 0.
So, if we take t = (r-s)/2, we get that t < 0.
But this is contradictory since t > 0 according to (1).
So, the only possibility is r = -s or (r+s)/2 = 0.
Or 0 is halfway between r and s.
So, both statements together are sufficient.
The correct answer is (C).
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