DelSingh wrote:
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Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?
(1) The coordinate of M is 1.5
(2) The coordinate of S is 6
From the GMAT Question pack 1
Rated: Hard
\(P = \frac{1}{3}(S+P)\) --------- P is 1/3 the distance between S and P
\(3P = S + P \)
\(2P = S\) ---------- twice the distance of P is S
\(P = \frac{1}{2}S\)
If we can determine the value of S, we can determine the coordinate of P.
(1) \(M = 1.5\)
\(M = \frac{-p + s}{2 }\)-------- M is the midway point between p and s. p is negative because its to the left of R, which is 0.
\(2M = -p + s\)
\(3 = \frac{-1}{2}s + s\)
\(3 = \frac{1}{2}s \)
\(6 = S\)
\(-3 = P\); SUFFICIENT.
(2) \(S = 6\)
\(-3 = P\); SUFFICIENT.
Answer is D.
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