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# On the number line shown, is zero halfway between r and s?

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On the number line shown, is zero halfway between r and s?

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The best way to answer this question is list all the possibilities. However simple the question looks, DONT do it in your head. Dont Tax your brain.

Case 1) All are on the Left of Zero. R < S < T < 0
Case 2) All are on the RHS of Zero 0 > R > S > T
Case 3) Scattered around the Zero. R< 0 < S < T or R< S < 0 < T
Now let us the pick up the first condition.
Stmt (1) S to the right of zero. Clearly this is not suff.
Stmt (2) The distance between t and r is the same as the distance between t and -s
This one is tricky, if not thought carefully.
Looking from the cases above, CASE (1) & CASE (2) are not applicable, because all are on one side of 0.
Now let us evaluate CASE 3
a) R < 0 < S < T
i.e. T + R = T + 2S=> S = -R ( YES)

b) R < S < 0 < T |S| < |T|
i.e. T + R = T - S => R = -S (YES)
c) R < S <<< 0 < T . |S| > |T|
i.e. T + R = S - T => 2T = S - R (NO)

Both the statements alone, do not solve provide a solution.
Let us try to combine them, If s is right of zero, this would help us answer the quesiton. Hence the answer is C

answered Mar 18, 2015 by Guru (5,628 points)
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Jyotsna Mehta