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Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: In the figure above, points P and T lie on line L. How many different [#permalink]

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15 Jul 2017, 06:35

Bharath99 wrote:

I think D.

2 such points are possible. Suppose X be the required point. X can be before P or X can be between P and T.

Note : X cannot be after T in the number line (as the dist btwn X and T cannot be twice the dist btwn X and P)

Yes correct there will be 2 such points and not one point.. I did a mistake by not analysing the point X between P and T . longhaul123 you can refer Bharath99 solution.. There will be 2 points.. So, D
_________________

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.

( 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.)

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.

( 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.

Yes I applied the same approach.(earlier i did a mistake though by taking only 1 point). Also no value is given for the points. So points may have decimal or integral values.

as u said the points may be fraction ____P____A______________T ____0____\(\frac{1}{3}\)_____________1

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

Let’s place a point Q on line L, such that point Q is twice as far from point T as it is from point P. We see that we can place Q somewhere i) to the left of P, ii) in between P and T, or iii) to the right of T. We need to see which of these 3 ways will make Q twice as far from point T as from point P.

To make things easier, let’s assume line L is a number line, and point P is at the number 3 and point T is at the number 6.

If we place point Q to the left of P, we can place it on the number 0 so that QP = |3 - 0| = 3 and QT = |6 - 0| = 6. We see that Q is twice as far from point T as from point P.

If we place point Q in between P and T, we can place it on the number 4 so that QP = |3 - 4| = 1 and QT = |6 - 4| = 2. We see that Q is also twice as far from point T as from point P.

If we place point Q to the right of T, there is no way we can make Q twice as far from point T as from point P, since Q is closer to T than to P (i.e., the distance between Q and T is always less than the distance between Q and P).

Thus, we have two locations to place Q such that Q is twice as far from point T as from point P.

Answer: D
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