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Options A or C cannot be correct answer since these points aren't even on segment PQ. E (1,0) is clearly closer to P, so it's also out, D is right in the middle of the segment, so only option B is left.

The question ask to divide the line PQ into 2:1 ratio and find the point. By symmetry, the line segment at x-axis (1,0) will be divided in ratio 1:2. Similarly, at (2,1) line will be divided in ration 2:1

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By looking at the figure it comes out that option "B" (2,1) is the right choice.

Re: In the figure above, the point on segment PQ that is twice a [#permalink]

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21 Dec 2012, 15:14

Sachin9 wrote:

twice as far from P as from Q

This confused me..I thought teh Qs is asking for the midpoint..

Could somebody explain me what it is asking..

and thanks bunuel for POE method. but how would u solve this algebraically?

I concur. I think it would be helpful if we can solve this algebraically using the given y-coordinate and point Q, rather than elimination — similar to Bunel's approach to this problem.
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Plugging values, we obtain answer as (2,1). Hence B

Once you know the formula its very easy.

P.S. Bunuel's approach is beautifully elegant. However, for me solving algebraically is much faster than figuring the answer choices out.
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Re: In the figure above, the point on segment PQ that is twice a [#permalink]

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30 Dec 2012, 02:10

I was thinking along those lines by forming a triangle and then solving it. This is a fairly easy question you can still use the answer choices but if its a bit more complicated I would like a fast approach.

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Plugging values, we obtain answer as (2,1). Hence B

Once you know the formula its very easy.

P.S. Bunuel's approach is beautifully elegant. However, for me solving algebraically is much faster than figuring the answer choices out.

This is called section formula. It will be helpful. Thanks
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Re: In the figure above, the point on segment PQ that is twice a [#permalink]

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20 Jan 2013, 02:11

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I think with questions like these, the test writers are testing whether you'd quickly jump to using an algebraic approach, which in this case is much more time consuming, as compared to making the answer choices a part of your toolbox for finding the correct answer.. The question itself tells us we need to split the line into 3 equal parts with the asked coordinate being 2 parts away from P A quick glance at the graph gives us the slope of 1, which easily shows us which points will cover the three segments P(0,-1) --> (1,0) --> (2,1) --> Q(3,2) Thus (2,1) being twice as far from P as from Q

True, an algebraic approach might be required for more complex problems where the slope isn't easily determined or the line segment might be split into a different ratio, but this question isn't testing that

Re: In the figure above, the point on segment PQ that is twice a [#permalink]

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06 Aug 2013, 01:41

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Coordinates of point P = (0,-1) Coordinates of point Q = (3,2) Point required to be found is on segment PQ that is twice as far from P as from Q So, adding (2,2) to point P (0,-1) Answer = B = (2,1)
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This is an interesting problem because, although we usually prefer an algebraic approach to solving GMAT questions, the quickest way to solve this problem is to analyze each answer choice in relation to the graph. We need to determine which answer choice gives us a point on the graph that is twice as far from P as from Q. This means that it is closer to Q than to P.

We are given that point Q is at (3,2) and point P is at (0,-1). Let’s start with answer choice A.

A) (3,1)

Looking at the graph we see that (3,1) is not even on line segment PQ. Answer choice A is not correct.

B) (2,1)

Looking at the graph we see that (2,1) is on line segment PQ and it is closer to Q than it is to P. We could use the distance formula to determine the actual distances, but let's wait to see if this is necessary. Let’s test the other answer choices to be certain that answer choice B is correct.

C) (2,-1)

Looking at the graph we see that (2,-1) is not even on line segment PQ. Answer choice C is not correct.

D) (1.5,0.5)

Looking at the graph we see that (1.5,0.5) is on line segment PQ; however, it appears to be about halfway between P and Q. Answer choice D is not correct.

E) (1,0)

Looking at the graph we see that (1,0) is on line segment PQ; however, it is closer to P than to Q. Answer choice E is not correct.
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