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Retired Moderator Joined: 29 Apr 2015
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In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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10 00:00

Difficulty:   55% (hard)

Question Stats: 59% (01:31) correct 41% (02:15) wrong based on 153 sessions

HideShow timer Statistics In the figure above, segments PQ and QR are each parallel to one of the coordinate axes. What is the ratio of the length of QR to PQ?

(1) The slope of the line that passes through points P and R is 0.75.
(2) The coordinates of point P are (4,2).

Attachment: Slope, ratio of sides.png [ 4.31 KiB | Viewed 4346 times ]

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Originally posted by reto on 13 Aug 2015, 10:33.
Last edited by Bunuel on 16 Aug 2015, 13:38, edited 1 time in total.
Edited the question.
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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Retired Moderator Joined: 29 Apr 2015
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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1
vinnisatija wrote:

Statement 1 is sufficient because it gives you the slope of the line. Ask yourself "what is the slope" of the line?

Slope = $$\frac{y2-y1}{x2-x1}$$

Now, y2-y1 is actually the same as PQ.

x2-x1 is the same as QR.

Therefore 1 alone is sufficient. Statement 2 gives you just one point, alone this is clearly insufficient.
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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vinnisatija wrote:

The question asks us to find the ratio QR/PQ which is equal to the slope of line PR. The reason why QR/PQ = slope of PR is shown in attached figure.

Statement 1 is sufficient as it directly gives the slope of line segment PR.

Statement 2 is NOT sufficient as with coordinates of 1 point (P) we can calculate the slope of line PR.

A is thus the correct answer.
Attachments image.jpg [ 24.16 KiB | Viewed 3841 times ]

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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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We should find legs ratio in the right triangle. We know that any ratio in right triangle depends only on the non-right angles degree and does not depend on the length of sides. So, we need only one angle degree

St.1 gives us such information

St.2 does not give any

A
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In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.

In the figure above, segments PQ and QR are each parallel to one of the coordinate axes. What is the ratio of the length of QR to PQ?

(1) The slope of the line that passes through points P and R is 0.75.
(2) The coordinates of point P are (4,2).

Transforming the original condition and the question using variable approach method, we can find QR:PQ=QR/PQ=1/slope of line PR(Since Q is a right-angle). Since we have the slope from 1), A is the answer.
Attachments Slope%2C ratio of sides.png [ 4.31 KiB | Viewed 3619 times ]

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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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can someone explain why ratio of legs is equal to the slope?
and why leg1/leg 2 = 1/slope and not leg2/leg1 = 1/slope?
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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2
mvictor wrote:
can someone explain why ratio of legs is equal to the slope?
and why leg1/leg 2 = 1/slope and not leg2/leg1 = 1/slope?

Hi mvictor:
There is simple formula to calculate the slope of a line:
Change in y / Change in x

In the above problem, to calculate change in y: we have to points of y i.e. y co-ordinate at point P and point Q (Don't worry about the actual value). Now if you substract these two values, you will get PQ (no matter whatever is the actual values).

Similarly you can find out the change in x i.e. QR

So Statement is actually provided the value for PQ / QR = 0.75. Using this value you can easily find out QR / PQ. Hence Stmt. I is sufficient.

In Stmt. II - we just have the x and y co-ordinates for point P. We can't find out the co-ordinates for other points. Hence not sufficient.

Hope it helps.

Hit kudos if you like the explanation!!

Thanks,
Chanakya
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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1
Lets assume P = (x1,y1)
R = (x2, y2)
Than Q = (x2,y1)
pq = sqrt((x2-x1)^2)
QR = sqrt((y2-y1)^2)

ratio of pq/qr = sqrt((x2-x1)^2)/ sqrt((y2-y1)^2)

We are given slope of line PR. Hence we are given ratio of (y2-y1)/(x2-x1)

hence sufficient.

Please give kudos if you like the explanation.
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Re: In the figure above, segments PQ and QR are each parallel to one of th  [#permalink]

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reto wrote: In the figure above, segments PQ and QR are each parallel to one of the coordinate axes. What is the ratio of the length of QR to PQ?

(1) The slope of the line that passes through points P and R is 0.75.
(2) The coordinates of point P are (4,2).

Attachment:
Slope, ratio of sides.png

st. 1:
We can use the linear equation to figure it out:

y=mx + c
y= 0.75x + c
=> c = y/0.75x (& since 0.75 = 3/4)
=> c = 4y/3x

st 2:
It's just one point in space. Not helpful.

Hence, A
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Hit Kudos to keep the community alive ! Re: In the figure above, segments PQ and QR are each parallel to one of th   [#permalink] 30 May 2019, 08:36
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