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

Bunuel Please provide a detailed pictorial explanation. Hard to understand how there is a right triangle. Thanks.

Hi sadikabid27

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

Please find the pictorial representation


Hope this helps you!

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): \(y+\sqrt{x^2+y^2}\) --> \(time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}\).

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!

Posted from my mobile device

Will questions like these appear in GMAT focus as they said Geometry has been removed?