Bunuel

In the figure above, points P and T lie on line L. How many different points on L are twice as far from point T as from point P?
(A) 6
(B) 4
(C) 3
(D) 2
(E) 1
Attachment:
2017-07-13_1028.png
I think the answer is D.
I assigned numbers.
After fooling around with the numbers, it was easier for me to use literal thirds, as in, \(\frac{1}{3}\)
FIRST SCENARIO: Let P = 0 and T = 1
________P___________________T
________0___________________1
Imagine A is the point twice as far from T as from P. First place A can be is BETWEEN P and T. A = \(\frac{1}{3}\)
____P____A______________T
____0____\(\frac{1}{3}\)_____________1
Distance from P to A: \(\frac{1}{3}\)
Distance from T to A: \(\frac{2}{3}\)
SCENARIO 2:
The second possible point for A is to the left of P.
Let T = \(\frac{1}{3}\), P = 0, and A = -\(\frac{1}{3}\).
__A________P________T
_-\(\frac{1}{3}\) _______0________\(\frac{1}{3}\)
Distance from P to A: \(\frac{1}{3}\)
Distance from T to A: \(\frac{2}{3}\)
That's all I can come up with. If point A lies to the right of T, I cannot construct any numbers that will work.
My intuition tells me that there is a problem with absolute value. If T is origin, and distance point is to the right of T, no point to the right of T will yield a distance twice as far from T as P.
Answer D
longhaul123, this should help with your question.
(
Bharath99, and
shashankism -- did you deploy some concept to which I do not refer here? I don't see any actual numbers, so I'm curious about your reasoning.)
Whew. I hope that's right, and I hope it helps.