Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Dec 1511:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
10 Oct 2019, 10:26
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
36% (02:23) correct
64%
(02:33)
wrong
based on 39
sessions
History
Date
Time
Result
Not Attempted Yet
A dog, a cat, and a mouse are at point A on triangle ABC. All three simultaneously run along triangle ABC, covering AB, then BC, and finally CA.
The dog moves at speed 12 on AB, 10 on BC, and 15 on CA.
The cat moves at speed 15 on AB, 15 on BC, and 10 on CA.
The mouse moves at speed 10 on AB, 20 on BC, and 12 on CA.
If all three finish at A at the same time, what is the measure of angle ABC?
A) 30
B) 45
C) 60
D) 90
E) 120
Source : MindYourDecisions
The dog moves at speed 12 on AB, 10 on BC, and 15 on CA.
The cat moves at speed 15 on AB, 15 on BC, and 10 on CA.
The mouse moves at speed 10 on AB, 20 on BC, and 12 on CA.
If all three finish at A at the same time, what is the measure of angle ABC?
A) 30
B) 45
C) 60
D) 90
E) 120
Source : MindYourDecisions
10 Oct 2019, 19:11
Kudos
Bookmarks
MahmoudFawzy
A dog, a cat, and a mouse are at point A on triangle ABC. All three simultaneously run along triangle ABC, covering AB, then BC, and finally CA.
The dog moves at speed 12 on AB, 10 on BC, and 15 on CA.
The cat moves at speed 15 on AB, 15 on BC, and 10 on CA.
The mouse moves at speed 10 on AB, 20 on BC, and 12 on CA.
If all three finish at A at the same time, what is the measure of angle ABC?
A) 30
B) 45
C) 60
D) 90
E) 120
Source : MindYourDecisions
The dog moves at speed 12 on AB, 10 on BC, and 15 on CA.
The cat moves at speed 15 on AB, 15 on BC, and 10 on CA.
The mouse moves at speed 10 on AB, 20 on BC, and 12 on CA.
If all three finish at A at the same time, what is the measure of angle ABC?
A) 30
B) 45
C) 60
D) 90
E) 120
Source : MindYourDecisions
Since time is the same, we can make three equations.
(1) \(\frac{x}{15}+\frac{y}{15}+\frac{z}{10}=\frac{x}{10}+\frac{y}{20}+\frac{z}{12}\)....Multiply both sides by 60, LCM of denominators
\(4x+4y+6z=6x+3y+5z......2x=y+z\)
(2) \(\frac{x}{15}+\frac{y}{15}+\frac{z}{10}=\frac{x}{12}+\frac{y}{10}+\frac{z}{15}\).....Multiply both sides by 60, LCM of denominators
\(4x+4y+6z=5x+6y+4z......x+2y=2z\)
(3) \(\frac{x}{10}+\frac{y}{20}+\frac{z}{12}=\frac{x}{12}+\frac{y}{10}+\frac{z}{15}\).....Multiply both sides by 60, LCM of denominators
\(6x+3y+5z=5x+6y+4z......x+z=3y\)
Subtract (3) from (2),
\(2y-z=2z-3y......5y=3z\)
Multiply (1) by 2 and subtract (2) from it
\(4x-x-2y=2y+2z-2z....3x-2y=2y.....3x=4y\)
Now we can find the ratio of all three sides.
\(3x=4y .....y=\frac{3x}{4}\) and \(5y=3z.....z=\frac{5y}{3}=\frac{5}{3}*\frac{3x}{4}=\frac{5x}{4}\)
So \(x:y:z=x:\frac{3x}{4}:\frac{5x}{4}=4x:3x:5x=4:3:5\), which is a triplet 3:4:5 in a right angled triangle.
We are looking for angle ABC, which is opposite to AC or z.
As z is the largest side, angle ABC will be the largest or 90, as 90 is the largest angle in a right angled triangle.
D
23 Oct 2024, 03:00
Kudos
Bookmarks
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
