Is |S-R|>|T-U|?

(1)|R-T|>|S-U|
(2)|R-U|>|S-T|



Make an effort to explain. It helps the new guys and me too!

thanks
praetorian

|S-R|>|T-U|?

(1)|R-T|>|S-U|
(2)|R-U|>|S-T|

Stem says
S-R > T-U or S-R<U-T
=> S+U> T+R or S+T<U+R

1) R+U>S+T or R-T<U-S => R+S<U+T ; insufficient

2) R-U>S-T or R-U<T-S
R+T>S+U or R+S<T+U; insufficient

together we can get both the conditions of the stem. Hence Ans=3, that is both taken together are sufficient.

Thanks Anand.
I tried to over simplify the problem.

I could not agree with you more. I am not sure I would have solved the question in two minutes. We definitely need shortcuts. I just feel that arriving at correct answer does not mean the method of solving the problem is correct. A slight twist in the question can make the solution invalid and can give you wrong answers.
I tried to put the solution because new comers can learn little bit about the absolute inequialities. I have learnt a lot from people like you by going through the post and I would like to contribute wherever I can.

Thanks,
Anand.

I think this problem should be approached in the following way. I know that the method looks very long but I think if understood once, it should not take long to do similar problems. In a way, it is just an extension of Racers approach.

We know that |x| = x, if x > 0 but |x| = -x if x < 0.

So any inquality |x| > |y| can result in the following possibilities:

x is +ve and y is +ve => x > y
x is -ve and y is -ve => -x > -y
x is +ve and y is -ve => x > -y
x is -ve and y is +ve => -x > y

Applying this logic, what we need to find here is Is |S-R|>|T-U|? In other words,

Is S-R > T-U? or
Is R-S > U-T? OR
Is S-R > U-T? OR
Is R-S > T-U? ========================(Q)

Now applying the logic to statement 1,

|R-T|>|S-U|, is this sufficient to say that ANY ONE of the above 4 possibilities is correct?

Let us see, this statement will give following possibilities

R-T > S-U => R-S > T-U (This is one of the possibilities in Q above. So the answer is YES)
T-R > U-S => S-R > U-T (So the answer is YES again)
R-T > U-S => R+S > T+U (Can not say )
T-R > S-U => T+U > S+R (Can not say)

Statement 1 NOT SUFF

Similarly statement 2 will give 4 possibilities, 2 of which will answer the question in YES and remaining 2 will not answer. So statement 2 NOT suff.

TOGETHER

Both the statments taken togethet will also result in the 4 possibilities that are mentioned in BOLD above.

So together NOT SUFF.

This will give answer E.

Can you guys comment on this method?

Akmai, can you also jump in here? Thanks