Bunuel wrote:

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.

_________________

At the still point, there the dance is. -- T.S. Eliot

Formerly genxer123