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07 Feb 2020, 07:45
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On a number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then what is the coordinate of T ?
A) 0
B) 1
C) 2
D) 3
E) 4
A) 0
B) 1
C) 2
D) 3
E) 4
07 Feb 2020, 17:28
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Bunuel
On a number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then what is the coordinate of T ?
A) 0
B) 1
C) 2
D) 3
E) 4
A) 0
B) 1
C) 2
D) 3
E) 4
Given:
1. On a number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively.
2. Suppose p < q < s < t, p = -1, s = 2.
Asked: If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then what is the coordinate of T ?
Since the distance between P and Q is twice the distance between Q and S; q = 1
Since S is the midpoint of Q and T; t=3
IMO D
shameekv1989
07 Feb 2020, 17:41
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On a number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then what is the coordinate of T ?
A) 0
B) 1
C) 2
D) 3
E) 4
p-----q-----s-----t
-1----q-----2-----t
distance between q and s = d
distance between p and q = 2d
Therefore PQ + QS = 3d = distance between PS = 3 -> d=1
Therefore distance between q and s is 1
Since S is the midpoint of q and t - distance between s and t = 1
Therefore coodinate of t = 2+1 = 3 - > Answer - D
A) 0
B) 1
C) 2
D) 3
E) 4
p-----q-----s-----t
-1----q-----2-----t
distance between q and s = d
distance between p and q = 2d
Therefore PQ + QS = 3d = distance between PS = 3 -> d=1
Therefore distance between q and s is 1
Since S is the midpoint of q and t - distance between s and t = 1
Therefore coodinate of t = 2+1 = 3 - > Answer - D
