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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure above, the point on segment PQ that is twice as far from

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Manhattan Prep Instructor G
Joined: 04 Dec 2015
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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herbgatherer wrote:
I felt the question is confusing. Shouldn't it be "In the figure above, the point on segment PQ that is half as far from P as from Q is"?

I think that you're reading it as a comparison between these two things:

- the distance between P and the new point
- the distance between P and Q

However, the wording of the problem is actually asking you to compare these two things:

- the distance between P and the new point
- the distance between the new point and Q
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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ccooley wrote:
herbgatherer wrote:
I felt the question is confusing. Shouldn't it be "In the figure above, the point on segment PQ that is half as far from P as from Q is"?

I think that you're reading it as a comparison between these two things:

- the distance between P and the new point
- the distance between P and Q

However, the wording of the problem is actually asking you to compare these two things:

- the distance between P and the new point
- the distance between the new point and Q

I found the wording of the question confusing, too.

The way I interpreted "twice as far from P as from Q" was "twice as far from P and twice as far from Q". That's what I feel the questions asks.
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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Do we need to assume that figures are drawn to scale in all the problems? Because I could answer this by just looking at the graph in few seconds.
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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santro789 wrote:
Do we need to assume that figures are drawn to scale in all the problems? Because I could answer this by just looking at the graph in few seconds.

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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Just visualize .. question says point on line PQ is such that it is twice as far from p than q. so it is near to q. scan through option.
Options A or C does not lie on segment PQ. E is clearly closer to P, so it is out, D is right in the middle of the segment, so only option B is left.
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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I got the midpoint between the two points (1,1) and then did a scan on answer choices. B looked the most plausible. It still took me 2:10 to digest and think about the question. Should have discarded A & C from the get-go.
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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Algebraic Solution:

Distance from P->Q:
a^2+b^2=c^2
(3)^2+(3)^2=c^2
18=c^2
sqrt(18)=c

Line is broken into three segments (given in the original question).
Therefore, each segment is equal to

sqrt(18)/3 = 1 segment
simplifying..
sqrt(2) = 1 segment

If we have 2 segments from P, we have
2* sqrt(2) = distance from P

Taking 2*sqrt(2) as the hypothenuse of a triangle, we can find out the X and Y sides of the triangle to give us the proper coordinates

x^2 + y^2 = (2*sqrt(2))^2
NOTE: x = y since this is isosceles triangle

2x^2 = (2 * sqrt(2))^2
2x^2 = 8
x^2 = 4
x = 2
y = 2

Add "2" to both the x and y axis to arrive at your point (2,1)

This method took ~ 2:30
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Re: In the figure above, the point on segment PQ that is twice as far from  [#permalink]

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[quote="Bunuel"] In the figure above, the point on segment PQ that is twice as far from P as from Q is

(A) (3,1)
(B) (2,1)
(C) (2,-1)
(D) (1.5,0.5)
(E) (1,0)

Practice Questions
Question: 43
Page: 158
Difficulty: 600

I found an alternate and quick way to do it .
step 1 : FIND THE EQUATION OF LINE . I got y = x -1 (for constant I picked a random point i.e 1 from the given line )
step 2 :Find pair of points that satisfy the equation . NOW YOU CAN CALCULATE the point that is 2 units away from Y on number line to cross check your ans . Re: In the figure above, the point on segment PQ that is twice as far from   [#permalink] 15 Oct 2019, 02:28

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