Problem Solving for 780+ Aspirants.

[This topic has 6 expert replies and 200 member replies]
Forum Index GMAT Math Problem Solving
Free $100 Amazon.com Gift Card - Buy a GMAT course using a Beat The GMAT discount code between Mar 8-22 and get a $100 Amazon.com Gift Card. Learn more!
Post New Topic   Post Reply

4meonly
GMAT Destroyer!

Default Avatar

Joined: 16 Aug 2008
Posts: 890

Thanks given: 20
Thanked 21 times in 21 posts

Target GMAT Score: 750)
GMAT Score: 660(
PostSun Feb 08, 2009 4:45 am
sureshbala
thank you!!!! Now clear! Yes, they really should be 45!!! Now I don not understand how I missed it - actuallym this rule with arcs is very easy Smile
Once again, thank you! I love this site for the opportunity to solve all difficulties! ))
_________________
4 Sale: GMAT Club Access
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostSun Feb 08, 2009 4:53 am
4meonly wrote:
sureshbala
thank you!!!! Now clear! Yes, they really should be 45!!! Now I don not understand how I missed it - actuallym this rule with arcs is very easy Smile
Once again, thank you! I love this site for the opportunity to solve all difficulties! ))
Nice to hear that you were able to recollect the basics...anyway...we have a lot to come in this thread....stay tuned.

Regards
Back to top
View user's profile Send private message
4meonly
GMAT Destroyer!

Default Avatar

Joined: 16 Aug 2008
Posts: 890

Thanks given: 20
Thanked 21 times in 21 posts

Target GMAT Score: 750)
GMAT Score: 660(
PostSun Feb 08, 2009 5:56 am
I will!!! Very Happy
_________________
4 Sale: GMAT Club Access
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostSun Feb 08, 2009 7:01 am
Folks, here is the next apple.....



In the above figure, PB/PC = 1/2 LCBA = 45° while LAPC = 60°. Find LACB.
Back to top
View user's profile Send private message
cjb
Rising GMAT Star

Default Avatar

Joined: 31 Oct 2008
Posts: 66

Thanks given: 5
Thanked 4 times in 4 posts
Location: London, UK

Test Date: 17 February 2009
Target GMAT Score: 770
GMAT Score: 770
PostSun Feb 08, 2009 9:58 am
sureshbala wrote:


In the above figure, ABC is a right angled triangle. Taking the hypotenuse AC a square is constructed. If O is the center of the square find angle ABO.
I didn't have a proper proof for this inside 2 minutes, but I think I could have guessed it correctly.

If the question was worded as above, then you could reasonably make ABC an isosceles right-angles triangle, without loss of generality. AC is then root-2 times as long as the other sides, and OB clearly bisects the angle ABC.

Similarly, imagine a right-angled triangle where BC is vanishingly small, so AC is only a tiny bit longer than AB. As AB gets smaller, then OB gets closer to OC, which is also 45 degrees.

Not beautiful maths, but enough for a confident guess.
_________________
80% of success is showing up -- Woody Allen

Last edited by cjb on Sun Feb 08, 2009 10:29 am; edited 1 time in total
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostSun Feb 08, 2009 10:11 am
sureshbala wrote:
Folks, here is the next apple.....



In the above figure, PB/PC = 1/2 LCBA = 45° while LAPC = 60°. Find LACB.
Folks, I hope this is keeping you busy....
Back to top
View user's profile Send private message
cjb
Rising GMAT Star

Default Avatar

Joined: 31 Oct 2008
Posts: 66

Thanks given: 5
Thanked 4 times in 4 posts
Location: London, UK

Test Date: 17 February 2009
Target GMAT Score: 770
GMAT Score: 770
PostSun Feb 08, 2009 10:54 am
sureshbala wrote:
sureshbala wrote:
Folks, here is the next apple.....



In the above figure, PB/PC = 1/2 LCBA = 45° while LAPC = 60°. Find LACB.
Folks, I hope this is keeping you busy....
I think I have a way to solve this, but it's not something I could reproduce in a test:

Drop a line from P to a new point, Q, on AB, such that LPQB = 90°. Triangle PQB is a right-angled isoscelese triangle, so length PQ = (length PB / root 2).

Now consider triangle PQA, with angles 15-75-90, and one side, PQ, with length given above:
sin 15° = PQ / PA

length PA = (1/(root 2)) / sin 15°

Now draw another new line, this one from C to AP, which it meets at R, such that LCRP = 90°. Triangle CRP is a 30-60-90 triangle, and CP is two units long, in the units we are using. Length CR is therefore (root 3), and length RP = 1.

Finally, triangle CRA is right-angled, and has two sides of length (root 3) and ((1/(root 2)) / sin 15°) - 1). Bizarrely, this second term also turns out to be (root 3), (and yes, I needed a calculator to know that). So it's also an isosceles right-triangle, and angle ACR is therefore 45°. This must be added to angle RCD, previously found to be 30°, to give

ACB = 75°

But like I said, I couldn't do this without a calculator and ten minutes. What's the trick?
_________________
80% of success is showing up -- Woody Allen
Back to top
View user's profile Send private message
cjb
Rising GMAT Star

Default Avatar

Joined: 31 Oct 2008
Posts: 66

Thanks given: 5
Thanked 4 times in 4 posts
Location: London, UK

Test Date: 17 February 2009
Target GMAT Score: 770
GMAT Score: 770
PostSun Feb 08, 2009 12:05 pm
sureshbala wrote:
angles made by two equal chords on the same segment of the circle are always equal.
Can you explain what this means? Over here:

http://www.craville.110mb.com/maths/circlegeometry.pdf

I read this:

"Angles in the same segment of a circle are equal."
- Sorry, I can't reproduce diagrams, I don't have any kind of drawing tool

I'm not sure what is meant by "segment" in this case? Can you explain it to me, or give me a link to a fuller explanation?

thanks!
James
_________________
80% of success is showing up -- Woody Allen
Back to top
View user's profile Send private message
cjb
Rising GMAT Star

Default Avatar

Joined: 31 Oct 2008
Posts: 66

Thanks given: 5
Thanked 4 times in 4 posts
Location: London, UK

Test Date: 17 February 2009
Target GMAT Score: 770
GMAT Score: 770
PostSun Feb 08, 2009 12:07 pm
Never mind, just found it here Embarassed :

http://www.mathsteacher.com.au/year10/ch06_geometry/09_angles_same_segment/segment.htm
_________________
80% of success is showing up -- Woody Allen
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostMon Feb 09, 2009 4:20 pm
sureshbala wrote:
Folks, here is the next apple.....



In the above figure, PB/PC = 1/2 LCBA = 45° while LAPC = 60°. Find LACB.
Folks, waiting for some more replies....anyway I will post the solution soon...keep trying
Back to top
View user's profile Send private message
TNgri
Just gettin' started!

Default Avatar

Joined: 07 Dec 2008
Posts: 3

Thanks given: 0
Thanked 0 times in 0 posts
PostMon Feb 09, 2009 9:16 pm
I wonder if the LABC is 90?
Back to top
View user's profile Send private message
gxliu
Just gettin' started!

Default Avatar

Joined: 23 Jun 2008
Posts: 21

Thanks given: 0
Thanked 2 times in 2 posts
PostTue Feb 10, 2009 7:09 am
LACB is 90. Since LAPC=60, LAPB=120. Since LAPB=120, LPAB=15.
Now you can figure out the angles of triangel ACP.
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostTue Feb 10, 2009 7:24 am
gxliu wrote:
LACB is 90. Since LAPC=60, LAPB=120. Since LAPB=120, LPAB=15.
Now you can figure out the angles of triangel ACP.
Dear gxliu....you were too quick in your conclusion....please check your calculation again.
Back to top
View user's profile Send private message
gxliu
Just gettin' started!

Default Avatar

Joined: 23 Jun 2008
Posts: 21

Thanks given: 0
Thanked 2 times in 2 posts
PostTue Feb 10, 2009 7:36 am
You're right. LACB is 45. I forgot to take into account the sides. tricky...
Back to top
View user's profile Send private message
sureshbala
GMAT Destroyer!



Joined: 04 Feb 2009
Posts: 318

Thanks given: 1
Thanked 65 times in 54 posts
Location: Delhi
PostTue Feb 10, 2009 7:43 am
gxliu wrote:
You're right. LACB is 45. I forgot to take into account the sides. tricky...
hmmm....you have to check again....
Back to top
View user's profile Send private message
Display posts from previous:   

Post New Topic   Post Reply All times are GMT - 7 Hours
Goto page Previous  1, 2, 3, ... 12, 13, 14  Next
Page 2 of 14
 
Forum Index GMAT Math Problem Solving
Most Active Members in Last 30 Days
1. harsh.champ 562 posts
2. shashank.ism 368 posts
3. thephoenix 319 posts
4. kstv 310 posts
5. ajith 279 posts
See More Top Beat The GMAT Members
Most Active Experts in Last 30 Days
1. lunarpower
Manhattan GMAT Teacher 		87 posts
2. Stuart Kovinsky
Kaplan GMAT Teacher 		63 posts
3. Lisa Anderson
Stacy Blackman Consulting 		54 posts
4. Testluv
Kaplan GMAT Teacher 		49 posts
5. Bryant@VeritasPrep
Veritas Prep 		41 posts
See More Top Beat The GMAT Experts