Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
10 May 2016, 19:06
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:44) correct
37%
(01:57)
wrong
based on 182
sessions
History
Date
Time
Result
Not Attempted Yet
In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 50 and the slope of line segment AC is 4/3, what is the length of AB?
A. 12
B. 18
C. 24
D. 28
E. 40
* A solution will be posted in two days.
A. 12
B. 18
C. 24
D. 28
E. 40
* A solution will be posted in two days.
Attachments
없음.png [ 7.94 KiB | Viewed 4352 times ]
10 May 2016, 20:38
Kudos
Bookmarks
Making things easy, lets take B at origin (0,0) and the triangle in II quadrant (because the hypotenuse needs to have +ve slope).
This gives us the coordinates of A: (0,y) and B: (-x,0)
Slope = 4/3
\(\frac{y-0}{0-(-x)} = \frac{4}{3}\)
\(\frac{y}{x} = \frac{4}{3}\)
y and x are in the ratio 4:3
y=4k and x=3k
Now, recall one of the most popular Pythagorean triplets- 3,4,5
Here, we already have two sides in ratio 3:4, so the third should be of the form 5k
Since AC=50, we get k=10
Hence, the other two sides are 30 and 40 respectively,
And AB = 40
Option E
This gives us the coordinates of A: (0,y) and B: (-x,0)
Slope = 4/3
\(\frac{y-0}{0-(-x)} = \frac{4}{3}\)
\(\frac{y}{x} = \frac{4}{3}\)
y and x are in the ratio 4:3
y=4k and x=3k
Now, recall one of the most popular Pythagorean triplets- 3,4,5
Here, we already have two sides in ratio 3:4, so the third should be of the form 5k
Since AC=50, we get k=10
Hence, the other two sides are 30 and 40 respectively,
And AB = 40
Option E
Attachments
Triangle-slope.jpg [ 995.88 KiB | Viewed 4231 times ]
10 May 2016, 21:19
Kudos
Bookmarks
MathRevolution
Hi,
AC is the hyp and is 50...
the slope = 4/3, meaning the vertical rise is 4, when horizontal move is 3..
so ratio of vertical/horizontal =\(\frac{AB}{BC} = \frac{4}{3}\)....
clearly the right triangle is of 3:4:5... Now 5 is 50 here, so AB , which is in ratio 4 will be 4*10 = 40
E
