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In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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37 00:00

Difficulty:   55% (hard)

Question Stats: 64% (01:55) correct 36% (02:03) wrong based on 848 sessions

### HideShow timer Statistics OG Q 2017 New Question

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Md. Abdur Rakib

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Magoosh GMAT Instructor G
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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8
AbdurRakib wrote: OG Q 2017 New Question

Dear AbdurRakib
Another good question. I am happy to respond. Statement #1: this gives us the length of OP, and we have the slope of PQ, but we have no idea how high Q goes. Because we don't know this, we can't compute the slope of OQ. This statement, alone and by itself, is insufficient.

Now, forget statement #1.

Statement #2: this gives us Q = (5,4). Well, we know O is at the origin, (0,0). We know this, because this is one thing we are allowed to assume from a coordinate geometry diagram: if a point looks like it is at the origin, and especially this point is given the name "O," then we can be sure that it is exactly at the origin. Thus, we know the coordinates of O & Q, so we can find the slope, m = 4/5. With this statement, we can directly compute an answer to the prompt question. This statement, alone and by itself, is sufficient.

First statement insufficient, second sufficient. Answer = (B)

Does all this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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B

this is a good question.

1)insuff

2) Q co-ordinaes are given and O is origin.So slope can be found

B
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GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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1
AbdurRakib wrote: OG Q 2017 New Question

Lets Assume P (a,b) and Q (x,y)
It is given that
Slope of OP
$$b/a=1/2$$
$$a=2b$$

Slope of OQ is $$y/x$$...Required..

Slope of PQ will be $$y-b/x-a = 2$$

y-b=2(x-2b)
y=2x-3b

(1)
OP = 2\sqrt{5}
OP = \sqrt{(a)^2 + (b^2)}
20 = a^2 + b^2
We already know a =2b
20 = 5b^2
b=+2 or -2
then a would be +4 or -4
If we use (4,2) to solve for (x,y) to reach to slope then
y-2/x-4 =2
y-2=2x-8
y=2x-6 We do not have another equation to solve for (x,y)

If we use (-4,-2) to solve for (x,y) to reach slope then
y+2/x+4 =2
y+2=2x+8
y=2x+6 We do not have another equation to solve for (x,y)

Hence Not Sufficient

(2) Q(5,4)--> x=5, y=4

y/x = 4/5

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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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mikemcgarry why are we allowed to assume that O is at origin?
Magoosh GMAT Instructor G
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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1
ambar09d wrote:
mikemcgarry why are we allowed to assume that O is at origin?

Dear ambar09d,

I'm happy to respond. My friend, on GMAT PS geometry diagrams, there are lots of special cases that we can't assume---we can assume parallel or right angles or two equal sides simply because something looks that way. "Almost" doesn't count in geometry.

Nevertheless, there are a few basic assumptions we can make. If a line looks straight, we can assume that it is straight, that is has no hidden bend or curve to it. Also, if a point is portrayed as "on" a line, we can assume that it is in fact, "on" the line and not simply near the the line. In this diagram, point O is shown at the juncture of the x- and y-axes. We absolutely can assume that it is on both of those lines, and therefore, must be the intersection, the origin. Also, conventionally, the origin is often labeled O. For a problem to have a point labeled O near the origin but not exactly on it would a level of deviousness that we simply don't see on the GMAT.

Does all this make sense?
Mike _________________
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Magoosh Test Prep

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GMAT 1: 730 Q50 V38 Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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ambar09d wrote:
mikemcgarry why are we allowed to assume that O is at origin?

Well x-axis and y-axis only meet at 1 point that is Origin with co-ordinate (0,0).

By figure O is marked at intersection of 2 axis so its the origin.
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GMAT 1: 730 Q50 V38 Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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1
Slope OP=1/2
Slope PQ=2
Find slope OQ
Assume p =(px,py)
Q= (qx,qy)
And as O is origin O= (0,0).

So slope OP py/px=1/2
slope PQ = (qy-py)/(qx-px) =2
Find slope qy/qx

1) it gives distance of OP =2root5
by distance formula px^2+py^2 =(2root5)^2
As py/px=1/2 => px=2py. Putting this value in above equation
=> 5py^2=20
=> py=2 => px=4

Putting these values in slope PQ => (qy-2)/(qx-4)=2
Not enough detail to find value of qx and qy or there ratios.

Not sufficient.

2) Direct co-ordinate of Q is given (5,4), so we cna find slope of line OQ.
Slope OQ = (5-0)/(4-0) = 5/4

Sufficient

Answer: B
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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i am confused. i think d is correct.

in 1
we now lengthe and slope we can find the coordinate of p
similarly we can find coordinate of q

and 1 is sufficient.
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GMAT 1: 730 Q50 V38 Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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thangvietnam wrote:
i am confused. i think d is correct.

in 1
we now lengthe and slope we can find the coordinate of p
similarly we can find coordinate of q

and 1 is sufficient.

Can you please try to find coordinates of Q using the information given in statement 1 and share the solution?

Check the detailed solution provided by Luckisnoexcuse, mikemcgarry and me. We have solved the question in detail and proved that statement 1 alone is not sufficient. So answer must be B.
And i think its official question, so you can check the solution from Official OG 2017 as well Magoosh GMAT Instructor G
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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thangvietnam wrote:
i am confused. i think d is correct.

in 1
we now lengthe and slope we can find the coordinate of p
similarly we can find coordinate of q

and 1 is sufficient.

Dear thangvietnam,

I'm happy to respond. From Statement #1, we are given the length of OP, and we already know the slope of OP, so we absolutely could find the (x, y) coordinates of point P. The trouble is that this is NOT what the question asks. It's asking for the slope of OQ, and having full information about OP and point P tells us zilch about point Q or segment OQ. From the prompt & Statement #1 combined, we know neither the length nor the slope of OQ--in fact, the question is asking for that slope.

Does all this make sense?
Mike _________________
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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mikemcgarry wrote:
Does all this make sense?
Mike Hi Mike
sorry but could you please clarify why knowing A is not enough?
we know the slope of OP, basically it's (y-0)/(x-0)= 1/2 or 2y=x
then we know the OP length which is 2\sqrt{5} or
OP=SQRT((x-0)^2+(y-0)^2)= 2sqrt5 then knowing that 2y= x
we can calculate and find y, then again knowing the slope 1/2 find x.

Then, knowing coordinates of point P (x,y) and the slope of line PQ = 2 we can find coordinates of point Q
then knowing those coordinates and coordinates of O (0,0) we can find the slope of OQ

It's more than 3 mins of calculations but still you will get there, what I'm missing here?
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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sorry Mike, got it, 2 variables x and y to find Q in one equality not possible to solve
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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mikemcgarry
Hi, I'm totally convinced that B is right answer.
Just want to ask further.
What if statement 1 gives the slope of line OP (eg: 2), can statement 1 alone also sufficient?
Thank you so much in advance Magoosh GMAT Instructor G
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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lichting wrote:
mikemcgarry
Hi, I'm totally convinced that B is right answer.
Just want to ask further.
What if statement 1 gives the slope of line OP (eg: 2), can statement 1 alone also sufficient?
Thank you so much in advance Dear lichting,

I'm happy to respond. From the prompt information, we only know one angle in the triangle, angle P. (We don't explicitly have the value of that angle, but with the slope information and trigonometry--beyond what the GMAT expects you to know, we could find that angle. As it happens, that angle is 143°7'48.368", but you don't need to know how to find that.) The point is, from the fact that the slopes of OP and PQ are determined and fixed, angle P is locked into place at a specific value. All we know from the prompt is that one angle.

As it is, Statement #1 gives us only a length--thus, for triangle OPQ we have one length and one angle, and we can't find anything from that combination.

Now, your question is confusing to me. You see, in any GMAT DS questions, 100% of the time, the information in the prompt alone, without the statements, is always always always insufficient. We can never give a definitive answer to the DS prompt question solely from information in the prompt--the statements may or may not provide sufficient information, but without the additional information in the statements, we never can get anywhere. Thus, any information already present in the prompt never gets us any closer to sufficiency. If the information we have at any point is not sufficient, then repeating any part of it does absolutely zilch for us. This is a very common human misunderstanding that advertising and politicians like to exploit: repeating something doesn't actually make it more true. Thus, repeating the slope of OP, which we already know, does't absolutely zero to enhance the sufficiency of statement #1.

Let's say the question were different, and the prompt were asking for, say, the length of PQ.
Then, if statement #1 told the length of OP and the slope of OQ, then from all three slope, we could find all the angles in the triangle, and with the value of the length, we could find all three sides. When I say "we could find them"--they are mathematical fixed with definite values as a result of that information, although finding the actual numerical lengths and angles would involve using trigonometry--again, beyond what the GMAT expects. Actually, this wouldn't be a real GMAT DS question, because the GMAT is scrupulous about not asking you to determine the sufficiency of quantities that are technically mathematically fixed, although the math to find them is beyond GMAT math: the GMAT DS never goes into that territory.

You may find this blog article relevant:
GMAT Data Sufficiency: Congruence Rules

Does all this make sense?
Mike _________________
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Magoosh Test Prep

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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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1
AbdurRakib wrote: OG Q 2017 New Question

Statement II:

This is straight forward. $$m = \frac{y2-y1}{x2-x1}$$ = $$\frac{4}{5}$$. So, Sufficient.

Statement I:

OP Line equation $$y = \frac{x}{2}$$
OQ Line equation $$y = 2x + c$$
We have, $$x^2 + y^2 = 20$$. Substitute, OP line equation in this.. we get $$P(8,4)$$
However, for finding OQ slope, we need Q coordinates which is not possible.

So, Insufficient.
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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Does point O always refer to the origin in GMAT? I originally answered E, as the question does not explicitly state that O is the origin.
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Re: In the figure above,line segment OP has slope 1/2 and line segment PQ  [#permalink]

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Why are we assuming point O is at the origin? Re: In the figure above,line segment OP has slope 1/2 and line segment PQ   [#permalink] 12 Oct 2018, 14:19
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# In the figure above,line segment OP has slope 1/2 and line segment PQ

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