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# In the figure above, points P and T lie on line L. How many different

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

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12 Jul 2017, 22:30
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Question Stats:

55% (01:08) correct 45% (01:15) wrong based on 79 sessions

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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 [ 1.94 KiB | Viewed 1353 times ]

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

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13 Jul 2017, 00:15
1
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

We are searching for points on L which is twice as far from P than from point T
means, P is the midpoint of T and the points which are being searched.

There is only one such possibility on line L.

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

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15 Jul 2017, 00:43
Can someone please help me with this question. I am not understanding why is P the midpoint of T?
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Re: In the figure above, points P and T lie on line L. How many different  [#permalink]

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15 Jul 2017, 02:39
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)
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Re: In the figure above, points P and T lie on line L. How many different  [#permalink]

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15 Jul 2017, 05:35
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
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In the figure above, points P and T lie on line L. How many different  [#permalink]

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15 Jul 2017, 10:39
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.

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

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20 Jul 2017, 01:45
genxer123 wrote:
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.

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.

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

__A________P________T
_-$$\frac{1}{3}$$ _______0________$$\frac{1}{3}$$

Similarly it can have integral values

____P____A______________T
____0____2_____________6

__A________P________T
_-2 _______0________2

Or,
____P____A______________T
____-2____0_____________4

__A________P________T
_2 _______6________10
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Re: In the figure above, points P and T lie on line L. How many different  [#permalink]

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25 Jul 2017, 10:44
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

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.

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

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13 Oct 2017, 01:43
Let us assume, the distance between Point p and Point t on line L is X.
<----x-->
p..............t

and the question asks how many points can be at a distance of 2x from point p,

that can be, as it is a linear line segment, p+2x or P-2x
hence, 2 points.
Re: In the figure above, points P and T lie on line L. How many different &nbs [#permalink] 13 Oct 2017, 01:43
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