Last visit was: 13 Dec 2024, 02:55 It is currently 13 Dec 2024, 02:55
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
metallicafan
User avatar
Retired Moderator
Joined: 04 Oct 2009
Last visit: 26 Aug 2020
Posts: 763
Own Kudos:
4,123
 []
Given Kudos: 109
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT & HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Posts: 763
Kudos: 4,123
 []
Two airplanes take off from one airfield at noon. One flies due east a 04 Nov 2010, 09:52
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

51% (02:28) correct 49% (02:45) wrong based on 140 sessions

History

Date
Time
Result
Not Attempted Yet
Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 13 Dec 2024
Posts: 15,543
Own Kudos:
70,231
 []
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,543
Kudos: 70,231
 []
Two airplanes take off from one airfield at noon. One flies due east a 04 Nov 2010, 19:43
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
metallicafan
Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566

This is the diagram I get from the information given. One plane due east 400 miles and other plane north-east 566 miles. Approximate answer is required.
Attachment:
Ques1.jpg
Ques1.jpg [ 4.58 KiB | Viewed 5263 times ]

My problem is that the only time when I know what to do with a 45 degree angle is when it is in a right triangle. But I do not know if this is a right triangle. But the good thing I know about GMAT is that they ask me questions based on some basic concepts only. They may twist the concepts so that it is hard to recognize but they will still test me on the same concepts. So I use this weakness of GMAT to find out whether this is a right triangle.
If it is a right triangle, its other two angles will be 45 each and hence AB will be 400. This means the hypotenuse will be \(400\sqrt{2}\). Since \(\sqrt{2}\) is close to 1.4, 400*1.4 = 560, close enough to 566. Hence the approximate value of AB is indeed 400 and this is a right angled triangle.
Of course, if this triangle weren't right angled, we could still get AB. Substitute 800 in place of 566 and try, if it interests you.
General Discussion
User avatar
Fijisurf
User avatar
Joined: 10 Sep 2010
Last visit: 26 Nov 2011
Posts: 89
Own Kudos:
169
Given Kudos: 7
Posts: 89
Kudos: 169
Two airplanes take off from one airfield at noon. One flies due east a 04 Nov 2010, 13:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
C

In two hours:
the plane flying East will be 400 miles away from airport.
the other plane will be 566 miles away from airport.

566/400 = ~1.4 = ~sqrt(2)

This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 400 miles apart.
User avatar
plk
User avatar
Joined: 27 Mar 2019
Last visit: 20 Oct 2020
Posts: 10
Own Kudos:
2
Given Kudos: 4
Posts: 10
Kudos: 2
Two airplanes take off from one airfield at noon. One flies due east a 13 Jul 2019, 15:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello everyone, I understood the solution, but i have a question:

How did we determine that was a right triangle? Thanks!
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Dec 2024
Posts: 1,859
Own Kudos:
7,093
 []
Given Kudos: 707
Location: India
Posts: 1,859
Kudos: 7,093
 []
Two airplanes take off from one airfield at noon. One flies due east a 13 Jul 2019, 22:05
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Angle between east and north-east direction is 45*
One angle is 45*
second angle=\(sin^{-1}(400/486)\)= 45*
Third angle= 180-45-45=90


plk
Hello everyone, I understood the solution, but i have a question:

How did we determine that was a right triangle? Thanks!
User avatar
plk
User avatar
Joined: 27 Mar 2019
Last visit: 20 Oct 2020
Posts: 10
Own Kudos:
2
Given Kudos: 4
Posts: 10
Kudos: 2
Two airplanes take off from one airfield at noon. One flies due east a 14 Jul 2019, 04:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816
Angle between east and north-east direction is 45*
One angle is 45*
second angle=\(sin^{-1}(400/486)\)= 45*
Third angle= 180-45-45=90


plk
Hello everyone, I understood the solution, but i have a question:

How did we determine that was a right triangle? Thanks!

Thanks for proving it in terms of trigonometry.
But, I guess, there is no need to use knowledge of this science solving GMAT tasks, isn't it?

So, seeing tasks like this we can just assume it is a right triangle as GMAT shouldnt test deep knowledge of maths, right?
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Dec 2024
Posts: 1,859
Own Kudos:
7,093
Given Kudos: 707
Location: India
Posts: 1,859
Kudos: 7,093
Two airplanes take off from one airfield at noon. One flies due east a 14 Jul 2019, 10:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
You can't assume anything in GMAT exam. We can solve it without even using trigonometry.

Draw a perpendicular BD on AC
In triangle BDC
\(BD^2+DC^2=BC^2\) (Pythagoras theorem)
BD=DC=\(400/\sqrt{2}\)

In triangle BDA

\(BD^2+DA^2=BA^2\) (Pythagoras theorem)
BD=\(400/\sqrt{2}\)
DA=\(586-(400/\sqrt{2})\)= \(400\sqrt{2}- (400/\sqrt{2})\)

\(BA^2= 400^2/2+2*400^2+400^2/2-2*400^2\)
\(BA^2=400^2\)
BA=400

A bit lengthy approach tho






plk
nick1816
Angle between east and north-east direction is 45*
One angle is 45*
second angle=\(sin^{-1}(400/486)\)= 45*
Third angle= 180-45-45=90


plk
Hello everyone, I understood the solution, but i have a question:

How did we determine that was a right triangle? Thanks!

Thanks for proving it in terms of trigonometry.
But, I guess, there is no need to use knowledge of this science solving GMAT tasks, isn't it?

So, seeing tasks like this we can just assume it is a right triangle as GMAT shouldnt test deep knowledge of maths, right?

Attachments

rgf.png
rgf.png [ 7.62 KiB | Viewed 2737 times ]

User avatar
SPatel1992
User avatar
Joined: 23 Jul 2015
Last visit: 14 Aug 2020
Posts: 66
Own Kudos:
33
Given Kudos: 297
Schools: Marshall '22 (S)
Schools: Marshall '22 (S)
Posts: 66
Kudos: 33
Two airplanes take off from one airfield at noon. One flies due east a 16 Jul 2019, 19:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
metallicafan
Two airplanes take off from one airfield at noon. One flies due east at 200 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

A. 166
B. 332
C. 400
D. 483
E. 566

This is the diagram I get from the information given. One plane due east 400 miles and other plane north-east 566 miles. Approximate answer is required.
Attachment:
Ques1.jpg

My problem is that the only time when I know what to do with a 45 degree angle is when it is in a right triangle. But I do not know if this is a right triangle. But the good thing I know about GMAT is that they ask me questions based on some basic concepts only. They may twist the concepts so that it is hard to recognize but they will still test me on the same concepts. So I use this weakness of GMAT to find out whether this is a right triangle.
If it is a right triangle, its other two angles will be 45 each and hence AB will be 400. This means the hypotenuse will be \(400\sqrt{2}\). Since \(\sqrt{2}\) is close to 1.4, 400*1.4 = 560, close enough to 566. Hence the approximate value of AB is indeed 400 and this is a right angled triangle.
Of course, if this triangle weren't right angled, we could still get AB. Substitute 800 in place of 566 and try, if it interests you.

Hi! I used a similar reasoning. I didn't know how to choose between B,C, and D. I chose D because it was closer to 500. How do I avoid this error in the future?
Moderator:
Bunuel
Math Expert
97864 posts