What is the value of x and y in terms of k

Question

A) x = ak/b; y = b-k
B) x = bk/a; y = a-k;
C) x = a-k; y = bk/a;
D) x =b-k; y= ak/b;
E) None of the above

LighthousePrep · Accepted Answer

Hi vatsavayi , First, we are going to assume the question asks for x and y in terms of k, a, and b. Questions on the GMAT won't be worded poorly. The best way to solve this problem is by diving in. We know that y = a - k because y is the height from the x-axis to the point (x,y), which is also the height from the origin to the point (0,a-k). The diagram shows how y + k = a. The only answer choice that has solution for y is B. Next, we want to find x. Because the two triangles share the angle created at (0,a), we know we have two similar triangles. One of the properties of similar triangles is that their side lengths will be proportional. See the diagram to help visualize this. Thus, x/k = b/a. With a little algebra we can see that x = bk/a . Answer choice B correctly shows both these solutions and is therefore the right answer. If you want to learn more about similar triangles, here is a good link: https://www.mathsisfun.com/geometry/tria ... milar.html, or you can feel free to reach out/ ask more questions. Hope this helps! Good luck studying!

arshu27 · Answer

using pythogoras theoram for the top smaller triangle i got the value of y=a+k. is there something wrong in my understanding?

Bunuel · Answer

Please show your work.

PareshGmat · Answer

There is no need to use Pythagoras theorem in this question for solution. Refer diagram below for calculation triangle.png Answer = B) x = bk/a; y = a-k;

arshu27 · Answer

Consider triangle ABC,
Using the distance formula we can find out AC which is sqrt(x^2+(y-a)^2).

using pythogoras theoram,

AC^2=BC^2 + AB^2.

therefore,

x^2+(y-a)^2=k^2 +x^2

Cancelling x^2 we get,

(y-a)^2=k^2

so k=y-a

y=k+a.

can you tell me what am i missing. Bunuel

KarishmaB · Answer

Co-ordinate geometry is best done with a hand made diagram.

Make the diagram of this question and label every point where any two lines intersect. What are the co-ordinates of the point opposite the hypotenuse of the smaller top triangle? The co-ordinates are (0, y). Why? Because the co-ordinates of the point in line with this one are (x, y). Since this line runs parallel to the x axis, the y co-ordinate will remain the same i.e. y.

From there, you directly get that y = a - k.

Anulitha · Answer

The question literally had two different solutions. Pythagorean theorem gives y=k+a and x=-bk/a. 
The other solution gives signs opposite to the solutions we get using Pythagorean theorem. Unless there's a reason why Pythagorean theorem cannot be used, not sure why we it's wrong.

Posted from my mobile device

KarishmaB · Answer

Because

(y-a)^2=k^2

so k=y-a
 
is wrong in the pythagorean solution given above.

When you square root, you get

|y - a| = |k|
Now we know that a is greater than y (since it is higher up on the y axis). So (y - a) is negative. 
So |y - a| = -(y - a) = a - y

Since k represents the distance, |k| = k

So a - y = k

y = a - k
Only correct answer.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the value of x and y in terms of k

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the value of x and y in terms of k

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards