November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 14 Mar 2011
Posts: 143

What is b in the circle shown above?
[#permalink]
Show Tags
Updated on: 27 Feb 2017, 21:50
Question Stats:
28% (03:01) correct 72% (02:37) wrong based on 420 sessions
HideShow timer Statistics
What is b in the circle shown above? (1) bc = 5a (2) The length of PQ is \(\sqrt{84}\) Attachment:
Capture.PNG [ 15.96 KiB  Viewed 4940 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If you find my posts/replies helpful, please take a moment to click on the "kudos" icon.
Originally posted by godot53 on 27 Feb 2017, 21:12.
Last edited by Bunuel on 27 Feb 2017, 21:50, edited 1 time in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 50670

Re: What is b in the circle shown above?
[#permalink]
Show Tags
27 Feb 2017, 21:50



Intern
Joined: 05 May 2016
Posts: 9

Re: What is b in the circle shown above?
[#permalink]
Show Tags
12 Mar 2017, 06:27
From the given data, 1) b is a common side to both the right angled triangles 2) Both the triangles have one common angle (90 degrees)
So, c/a = b/b => c=a
And by using Pythagoras theorem, 84= (b*b) + (5 * 5)
Hence Statement 2 alone is sufficient.
Kudos +1 guys!



Manager
Joined: 16 Jan 2017
Posts: 63

Re: What is b in the circle shown above?
[#permalink]
Show Tags
12 Mar 2017, 08:49
hey, I am confused as to c=a in this case. could you explain this?



Intern
Joined: 05 Oct 2016
Posts: 1

Re: What is b in the circle shown above?
[#permalink]
Show Tags
12 Mar 2017, 19:46
Confused as well. Detailed explanation will be helpful.



Intern
Joined: 18 Aug 2014
Posts: 49
Location: India
GPA: 3.11

Re: What is b in the circle shown above?
[#permalink]
Show Tags
12 Mar 2017, 20:36
vmelgargalan wrote: hey, I am confused as to c=a in this case. could you explain this? The STE 1 can be made from the figure using the theory of similar triangles. using Pythagorean theory we can make an equation with only one variable. B is sufficient
_________________
Today's actions are tomorrow's results



Manager
Joined: 23 Jul 2015
Posts: 156

What is b in the circle shown above?
[#permalink]
Show Tags
14 Mar 2017, 04:55
JanarthCj wrote: From the given data, 1) b is a common side to both the right angled triangles 2) Both the triangles have one common angle (90 degrees)
So, c/a = b/b => c=a
And by using Pythagoras theorem, 84= (b*b) + (5 * 5)
Hence Statement 2 alone is sufficient.
Kudos +1 guys! per your logic, each triangle inscribed in a circle is a isosceles right triangle. I think you are confusing it with another property or similar triangles i.e ratio of area = square of the ratio of sides



Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 496
Location: India

Re: What is b in the circle shown above?
[#permalink]
Show Tags
15 Mar 2017, 04:15
from the similar triangle we can say that b/5 = a/c or bc =5a and c^2 = b^2 + 5^2 St 1: bc=5a. Mentioned above. INSUFFICIENT St 2: a = √84 therefore bc = 5√84 and c^2 = b^2 +25. two variable, two equation. SUFFICIENT Option B
_________________
GMAT Mentors



Intern
Joined: 24 Jul 2016
Posts: 1

Re: What is b in the circle shown above?
[#permalink]
Show Tags
12 Jul 2017, 13:59
JanarthCj wrote: From the given data, 1) b is a common side to both the right angled triangles 2) Both the triangles have one common angle (90 degrees)
So, c/a = b/b => c=a
And by using Pythagoras theorem, 84= (b*b) + (5 * 5)
Hence Statement 2 alone is sufficient.
Kudos +1 guys! Could you please explain how do you know that the triangles are similar? Based on the given information, don't you need to confirm that an additional pair of sides is similar, or that an additional pair of angles is equal? Thank you!



Intern
Joined: 16 Apr 2017
Posts: 45

What is b in the circle shown above?
[#permalink]
Show Tags
21 Jul 2017, 11:13
godot53 wrote: What is b in the circle shown above? (1) bc = 5a (2) The length of PQ is \(\sqrt{84}\) Attachment: The attachment Capture.PNG is no longer available From the information and attached figure we can derive: angle PQR = angle QOR = 90 degrees (1) angle PRQ = angle QRO = x degrees (2) From 1 and 2 and AAA similarity ===> angle QPR = angle QQR = y degrees Therefore the triangles PQR and QOR are similar PQ/QR = QO/OR ==> a/c = b/5 ==> bc =5a.........(3) Statement 1 ==> Same as can be derived from given information and insufficient since various combinations exist Statement 1 ==> From (3), a = √84 and b^2 + 5^2 = C^2 (since QOR is a right angle triangle) we can get the value of b
Attachments
Fig1.jpg [ 129.96 KiB  Viewed 3338 times ]
_________________
KUDOS please, if you like the post or if it helps



Manager
Joined: 22 Aug 2016
Posts: 83
Location: India
Concentration: Operations, Finance
GMAT 1: 650 Q49 V29 GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Other (Education)

Re: What is b in the circle shown above?
[#permalink]
Show Tags
21 Jul 2017, 19:29
Supermaverick wrote: godot53 wrote: What is b in the circle shown above? (1) bc = 5a (2) The length of PQ is \(\sqrt{84}\) From the information and attached figure we can derive: angle PQR = angle QOR = 90 degrees (1) angle PRQ = angle QRO = x degrees (2) From 1 and 2 and AAA similarity ===> angle QPR = angle QQR = y degrees Therefore the triangles PQR and QOR are similar PQ/QR = QO/OR ==> a/c = b/5 ==> bc =5a.........(3) Statement 1 ==> Same as can be derived from given information and insufficient since various combinations exist Statement 1 ==> From (3), a = √84 and b^2 + 5^2 = C^2 (since QOR is a right angle triangle) we can get the value of b Please explain how do we find the value of 'b'



Intern
Joined: 18 Jul 2017
Posts: 2

Re: What is b in the circle shown above?
[#permalink]
Show Tags
06 Sep 2017, 08:39
with a value as rt(84), we can find the value of diameter in terms of x+5 for triangle PQR and using the A value we can find length of x in terms of b and so on create a equation and by solving it we will get b x as 7 and b as rt(35).



Intern
Joined: 11 Oct 2017
Posts: 27

What is b in the circle shown above?
[#permalink]
Show Tags
10 Nov 2017, 08:19
I got it wrong but I'll provide my approach after thinking about it, to see if I can help.
Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5bc, angles Q,R,90º. Looks like 306090 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "306090, x x√3, 2x" or Pitagoras.
Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient > BCE
2) PQ = √84 One side! So can apply pitagoras and "306090" Can find C! with C then can find b with pitagoras. Sufficient > B



Manager
Joined: 24 Jun 2017
Posts: 122

Re: What is b in the circle shown above?
[#permalink]
Show Tags
16 Nov 2017, 21:16
ByjusGMATapp wrote: from the similar triangle we can say that b/5 = a/c or bc =5a and c^2 = b^2 + 5^2
St 1: bc=5a. Mentioned above. INSUFFICIENT St 2: a = √84 therefore bc = 5√84 and c^2 = b^2 +25. two variable, two equation. SUFFICIENT
Option B Seems like you made your mind bc = 5√84 this is not right You are taking bc=5a from the 1st statement and assuming that statement 2 alone is enough. Can somebody please provide a clear answer, why B and not C?



Manager
Joined: 24 Jun 2017
Posts: 122

What is b in the circle shown above?
[#permalink]
Show Tags
16 Nov 2017, 21:19
PaterD wrote: I got it wrong but I'll provide my approach after thinking about it, to see if I can help.
Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5bc, angles Q,R,90º. Looks like 306090 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "306090, x x√3, 2x" or Pitagoras.
Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient > BCE
2) PQ = √84 One side! So can apply pitagoras and "306090" Can find C! with C then can find b with pitagoras. Sufficient > B Your entire solution is based that it's 306090, triangle, which we don't know



Intern
Joined: 11 Oct 2017
Posts: 27

Re: What is b in the circle shown above?
[#permalink]
Show Tags
17 Nov 2017, 05:50
cbh wrote: PaterD wrote: I got it wrong but I'll provide my approach after thinking about it, to see if I can help.
Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5bc, angles Q,R,90º. Looks like 306090 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "306090, x x√3, 2x" or Pitagoras.
Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient > BCE
2) PQ = √84 One side! So can apply pitagoras and "306090" Can find C! with C then can find b with pitagoras. Sufficient > B Your entire solution is based that it's 306090, triangle, which we don't know I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90 60  30 Side measures: 2x  x√3  x Is similar for equilateral: Angle measures: 90 45  45 Side measures: x√2  x  x Still the more possible approaches the better, this one is a hard one



Manager
Joined: 24 Jun 2017
Posts: 122

What is b in the circle shown above?
[#permalink]
Show Tags
17 Nov 2017, 06:08
PaterD wrote: I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90 60  30 Side measures: 2x  x√3  x
Is similar for equilateral: Angle measures: 90 45  45 Side measures: x√2  x  x
Still the more possible approaches the better, this one is a hard one I meant you can't know if it's 90 60 30 or 90 45 45 or any other angle combination https://en.wikipedia.org/wiki/Thales%27 ... heorem.gifYou just know that this is right triangle. That's it Actually there are 3 right triangles, which are similar to each other, so basically that kind of question could be solved through similarity but I don't see how that can be solved via option B only Bunuel wrote: can you please elaborate it? I'm confused a bit, much appreciated!



Intern
Joined: 11 Oct 2017
Posts: 27

Re: What is b in the circle shown above?
[#permalink]
Show Tags
17 Nov 2017, 08:23
cbh wrote: PaterD wrote: I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90 60  30 Side measures: 2x  x√3  x
Is similar for equilateral: Angle measures: 90 45  45 Side measures: x√2  x  x
Still the more possible approaches the better, this one is a hard one I meant you can't know if it's 90 60 30 or 90 45 45 or any other angle combination https://en.wikipedia.org/wiki/Thales%27 ... heorem.gifYou just know that this is right triangle. That's it Actually there are 3 right triangles, which are similar to each other, so basically that kind of question could be solved through similarity but I don't see how that can be solved via option B only Bunuel wrote: can you please elaborate it? I'm confused a bit, much appreciated! Dude you are right.... I assumed the angle measures I'll call some cavalry to solve this as I can't see a proper way to crack this nut VeritasPrepKarishma could you please help us with this?



Intern
Joined: 07 Apr 2018
Posts: 8
Location: India
Concentration: Technology, Strategy
WE: Engineering (Computer Software)

Re: What is b in the circle shown above?
[#permalink]
Show Tags
06 Aug 2018, 07:34
Took a lot of time, but here's my solution.
From the diagram, say the diameter is d b^2+25 = c^2, b^2+(d5)^2=a^2 & d^2=a^2+c^2.
Using the 3 equations it can be resolved to c^2=5d, telling the 2 triangles are similar to one other.
Statement 1: bc=5a gives us the same info as above, unless we know one of the other sides we cannot solve for b. This is insufficient.
Statement 2: a^2=84, put this into the d^2=a^2+c^2 along with c^2=5d. These will resolve to a value for d from which one can solve for b. Sufficient
Please comment if you see any flaws in the above method or ways of making this faster.




Re: What is b in the circle shown above? &nbs
[#permalink]
06 Aug 2018, 07:34






