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# P, Q and R are located in a flat region of a certain state.

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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
Bunuel Please provide a detailed pictorial explanation. Hard to understand how there is a right triangle. Thanks.
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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
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Bunuel Please provide a detailed pictorial explanation. Hard to understand how there is a right triangle. Thanks.

Since the point Q is
1. y miles due north of R
2. x miles due east of P
and are connected via straight roads, the points PQR form a right-angled triangle

Attachment:

Diagram.png [ 3.17 KiB | Viewed 12153 times ]

Hope this helps you!
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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
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Bunuel wrote:
MensaNumber wrote:
are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z

P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)

A. $$\frac{\sqrt{x^2+y^2}}{z}$$

B. $$\frac{x+\sqrt{x^2+y^2}}{z}$$

C. $$\frac{y+ \sqrt{x^2+y^2}}{z}$$

D. $$\frac{z}{x+\sqrt{x^2+y^2}}$$

E. $$\frac{z}{y+\sqrt{x^2+y^2}}$$

Points are located as shown below:

P----Q
------
------
-----R

So we have the right triangle: $$PQ=x$$ and $$QR=y$$. $$PR=hypotenuse=\sqrt{x^2+y^2}$$.

Total distance to cover: $$y+\sqrt{x^2+y^2}$$ --> $$time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}$$.

Bunuel we are asked to find Q to R and R to P , in other words TWO LINES , why do you use $$PQ=x$$

and where from do you get Y which is not under radical sign ? $$y+\sqrt{x^2+y^2}$$

thank you
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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
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dave13 wrote:
Bunuel wrote:
MensaNumber wrote:
are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z

P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)

A. $$\frac{\sqrt{x^2+y^2}}{z}$$

B. $$\frac{x+\sqrt{x^2+y^2}}{z}$$

C. $$\frac{y+ \sqrt{x^2+y^2}}{z}$$

D. $$\frac{z}{x+\sqrt{x^2+y^2}}$$

E. $$\frac{z}{y+\sqrt{x^2+y^2}}$$

Points are located as shown below:

P----Q
------
------
-----R

So we have the right triangle: $$PQ=x$$ and $$QR=y$$. $$PR=hypotenuse=\sqrt{x^2+y^2}$$.

Total distance to cover: $$y+\sqrt{x^2+y^2}$$ --> $$time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}$$.

Bunuel we are asked to find Q to R and R to P , in other words TWO LINES , why do you use $$PQ=x$$

and where from do you get Y which is not under radical sign ? $$y+\sqrt{x^2+y^2}$$

thank you

You don't read questions carefully enough.

The question asks to find the number of hours need to drive from Q to R and then from R to P at a constant rate of z miles per hour, NOT the distance.

Total distance to cover (in blue): $$y+\sqrt{x^2+y^2}$$ --> $$time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}$$.

Attachment:

Untitled.png [ 4.79 KiB | Viewed 11926 times ]
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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
If you already know the Algebraic solution to this Problem, when you REVIEW, YOU SHOULD TRY ANOTHER APPROACH!

This is a Variable in the choices type question.so this is a great question to TEST IT! Try your own number.

So let's try some nice small numbers:

The speed z = 2,
The three sides:
1/ side P to Q >> x = 4,
2/ side Q to R >> y = 3 and
3/ thus the hypotenuse side P to R will be
5. Pythagorean triplet!!
(With enough official question practice the intuition to use smart number will develop)

Now we want to go: Q to R and then R to P.
Basically this means we want to go (3+5)=8 miles total. Our speed z is 2 miles per hour. So we will need total 4 hours.
So our Target value is 4

Let's find 4 when we plug in x=4, y=3 and z=2.

Taking a small glance in the answer choices, we can see all choices contain [√(x^2 + y^2)]
^^this is equal to [√(4^2 + 3^2)] = √25 = 5.

(A) 5/2 nope.
(B) 9/2 nope.
(C) (3+5)/2 = 4 BINGO!
(D) this is less than 1
(E) this is also less than 1.

DONE!

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Re: P, Q and R are located in a flat region of a certain state. [#permalink]
Will questions like these appear in GMAT focus as they said Geometry has been removed?
Re: P, Q and R are located in a flat region of a certain state. [#permalink]
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