Apr 20 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Apr 20 10:00 PM PDT  11:00 PM PDT The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale! Apr 21 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Apr 21 10:00 PM PDT  11:00 PM PDT $84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED Apr 22 08:00 AM PDT  09:00 AM PDT 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. Save your spot today! Apr 23 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, April 23rd at 8 pm ET Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54371

P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 06:13
Question Stats:
63% (01:45) correct 37% (01:52) wrong based on 146 sessions
HideShow timer Statistics
P is a circle with radius r. If AB is a chord in circle P, is AB<6? (1) r=5 (2) The height from the center of P to AB is smaller than 4.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Senior Manager
Joined: 23 Apr 2015
Posts: 300
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 07:32
Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. 1) with radius r =5, we can't tell whether AB < 6, Not sufficient Eliminate A and D 2) The height from centre of P to AB is smaller than 4. we can assume AB=6 and then use Pythagoras theorem, but we dont know the radius. Not sufficient , Eliminate B 1) + 2), Sufficient, use Pythagoras theorem Answer is C



Retired Moderator
Joined: 26 Nov 2012
Posts: 591

P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
Updated on: 14 Sep 2016, 12:02
Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. Stat 1: Diameter is 10 and it is the longest chord. if AB is very near to diameter then AB > 6...if AB is somewhere at the bottom of circle it can be lesser than 6...Insufficient. Stat 2: We have information about distance between diameter and chord and it is not exact distance and we are not sure about radius too..Insufficient. Stat 1+2: When r = 5 and distance b/w diameter and chord is 1 or 2 or 3. Then we get right angled triangle, for example let's assume distance is 4( which is maximum) then we get other side as 3, then total is 6. For maximum distance we are getting AB as 6 then for lesser than 4 value we clearly get AB > 6...Sufficient. IMO option C.
Originally posted by msk0657 on 14 Sep 2016, 07:45.
Last edited by msk0657 on 14 Sep 2016, 12:02, edited 2 times in total.



Intern
Joined: 13 Jan 2016
Posts: 46

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 08:10
What happens if the height from the center is 0? Then AB becomes the diameter and it will be 10. I think it is E.



Retired Moderator
Joined: 26 Nov 2012
Posts: 591

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 08:33
ruggerkaz wrote: What happens if the height from the center is 0? Then AB becomes the diameter and it will be 10. I think it is E. We are clearly given that there is a chord on the circle , then your point is not valid.



Intern
Joined: 13 Jan 2016
Posts: 46

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 09:00
MSK, in your opinion, the AB is always greater than 6? If the height is 0.1 and the diameter is 10, the chord will be very close to the diameter. At the same time, if the height is 3.9 and the radius is 5, the portion of the chord which is hypotenuse will be over 6. My assumption is that the height from the center is intersecting the chord AB. Thanks for clearing this up for me.



Director
Joined: 05 Mar 2015
Posts: 999

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 11:10
msk0657 wrote: Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. Stat 1: Diameter is 10 and it is the longest chord. if AB is very near to diameter then AB > 6...if AB is somewhere at the bottom of circle it can be lesser than 6...Insufficient. Stat 2: We have information about distance between diameter and chord and it is not exact distance and we are not sure about radius too..Insufficient. Stat 1+2: When r = 5 and distance b/w diameter and chord is 1 or 2 or 3. Then we get right angled triangle, for example let's assume distance is 4( which is maximum) then we get other side as 3, then total is 6. For maximum distance we are getting AB as 6 then for lesser than 4 value we clearly get AB < 6...Sufficient. IMO option C. i think the highlighted portion is wrong...we get always AB>6 for h<4 even if h=0 as diameter is also a chord.. Ans C



Intern
Joined: 13 Jan 2016
Posts: 46

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 11:23
I am having a hard time understanding how the length of the chord can be greater than 6 in the attached image. Can someone please clear this up for me? Thanks!!
Attachments
Circle.png [ 8.69 KiB  Viewed 1260 times ]



Director
Joined: 05 Mar 2015
Posts: 999

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 11:28
ruggerkaz wrote: I am having a hard time understanding how the length of the chord can be greater than 6 in the attached image. Can someone please clear this up for me?
Thanks!! height should be 90 deg. from radius or dia....



Director
Joined: 05 Mar 2015
Posts: 999

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 11:32
ruggerkaz wrote: I am having a hard time understanding how the length of the chord can be greater than 6 in the attached image. Can someone please clear this up for me?
Thanks!! fig should be like below one
Attachments
circ.png [ 8.1 KiB  Viewed 1245 times ]



Retired Moderator
Joined: 26 Nov 2012
Posts: 591

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 12:02
rohit8865 wrote: msk0657 wrote: Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. Stat 1: Diameter is 10 and it is the longest chord. if AB is very near to diameter then AB > 6...if AB is somewhere at the bottom of circle it can be lesser than 6...Insufficient. Stat 2: We have information about distance between diameter and chord and it is not exact distance and we are not sure about radius too..Insufficient. Stat 1+2: When r = 5 and distance b/w diameter and chord is 1 or 2 or 3. Then we get right angled triangle, for example let's assume distance is 4( which is maximum) then we get other side as 3, then total is 6. For maximum distance we are getting AB as 6 then for lesser than 4 value we clearly get AB < 6...Sufficient. IMO option C. i think the highlighted portion is wrong...we get always AB>6 for h<4 even if h=0 as diameter is also a chord.. Ans C Yes...that is typo mistake...



Manager
Joined: 01 Sep 2016
Posts: 52

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 12:22
seems to be C to mee too,.... Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4.



Intern
Joined: 13 Jan 2016
Posts: 46

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 13:06
got it now. thanks for clearing this up everyone.



VP
Joined: 30 Jan 2016
Posts: 1010

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
14 Sep 2016, 21:22
C. If height equals to 4, then half of the chord equals to 3 (2516=9). So the chord is 6 As the height is getting lower, i.e. 3, the half of the chord equals 4. So the chord is 8. SO the chord is less than 6
_________________



Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 230
Location: India
Concentration: Strategy, Operations
GPA: 4
WE: Consulting (Manufacturing)

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
16 Sep 2016, 08:27
Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. a I go with E : Reasons: Fixed AB = 3.9 R = 5 , one more side is X. in a triangle sum of the two sides > third side We know 2*X = AB (chord gets bisected from centre) 1)X = 2.9, AB = 3.9, R = 5 we can form a triangle so here AB = 2*2.9 = 5.8 and it is <6 2)X = 3.1, AB = 3.9, R = 5 we can form a triangle so here AB = 2*3.1 = 6.2and it is >6 Hope I didn't make any mistake.
_________________
Aiming for a 3 digit number with 7 as hundredths Digit



Director
Joined: 05 Mar 2015
Posts: 999

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
16 Sep 2016, 11:28
Balajikarthick1990 wrote: Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. a I go with E : Reasons: Fixed AB = 3.9 R = 5 , one more side is X. in a triangle sum of the two sides > third side We know 2*X = AB (chord gets bisected from centre) 1)X = 2.9, AB = 3.9, R = 5 we can form a triangle so here AB = 2*2.9 = 5.8 and it is <6 2)X = 3.1, AB = 3.9, R = 5 we can form a triangle so here AB = 2*3.1 = 6.2and it is >6 Hope I didn't make any mistake. Didnt get ur explanation...(highlighted parts) can u post the solution image



Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 230
Location: India
Concentration: Strategy, Operations
GPA: 4
WE: Consulting (Manufacturing)

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
16 Sep 2016, 11:41
rohit8865 wrote: Balajikarthick1990 wrote: Bunuel wrote: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4. a I go with E : Reasons: Fixed AB = 3.9 R = 5 , one more side is X. in a triangle sum of the two sides > third side We know 2*X = AB (chord gets bisected from centre) 1)X = 2.9, AB = 3.9, R = 5 we can form a triangle so here AB = 2*2.9 = 5.8 and it is <6 2)X = 3.1, AB = 3.9, R = 5 we can form a triangle so here AB = 2*3.1 = 6.2and it is >6 Hope I didn't make any mistake. Didnt get ur explanation...(highlighted parts) can u post the solution image Sorry my bad and thanks for pointing: Total chord is AB. Since we drop a perpendicular from centre. The chord gets bisected  So (AB/2) 1)X = 2.9, (AB)/2 = 3.9, R = 5 we can form a triangle so here AB = 2*2.9 = 5.8 and it is <6 2)X = 3.1, (AB)/2= 3.9 , R = 5 we can form a triangle so here AB = 2*3.1 = 6.2 and it is >6
_________________
Aiming for a 3 digit number with 7 as hundredths Digit



Director
Joined: 05 Mar 2015
Posts: 999

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
16 Sep 2016, 19:30
Didnt get ur explanation...(highlighted parts) can u post the solution image[/quote]
Sorry my bad and thanks for pointing:
Total chord is AB. Since we drop a perpendicular from centre. The chord gets bisected  So (AB/2)
1)X = 2.9, (AB)/2 = 3.9, R = 5 we can form a triangle so here AB = 2*2.9 = 5.8 and it is <6
2)X = 3.1, (AB)/2= 3.9 , R = 5 we can form a triangle so here AB = 2*3.1 = 6.2 and it is >6[/quote]
if you r droping a perpendicular ,then it must be a right triangle... So for statement 1 u need to recheck ur calculations...



Board of Directors
Joined: 17 Jul 2014
Posts: 2556
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
15 Aug 2017, 15:35
from 1, we get 5<AB<10. so it might be true, but might not be true. not sufficient. from 2 alone, we get the h, but no info on R...
from 1 and 2, we can draw 2 right triangles with a leg of <4, and hypotenuse of 5. let's take 2 extremes...leg =4 and leg =0. if leg =0, we know for sure AB>6. if leg is 4, it is still >6. so in any case, AB > 6.
C is the answer.



Manager
Joined: 13 Mar 2013
Posts: 162
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
Show Tags
17 Aug 2017, 20:49
This is a Yes/No DS question. The issue is whether AB<6. Stat. (1) alone: Knowing the radius does nothing to pinpoint the location and length of chord AB. AB could be a longer than 6 (e.g.  the diameter=2r=10), or smaller than 6. Therefore, Stat. (1)>Maybe>IS>BCE Stat. (2) alone: Drawing a height to AB creates a right triangle, which might be helpful in determining the length of its various legs using the Pythagorean theorem. However, since the Pythagorean theorem needs 2 sides of a right triangle to find the third, and stat. (2) alone gives you a range of only one side, it is insufficient  AB could still be greater or smaller than 6. Stat. (2)>MAYBE>ISCE (1) and (2) combined are sufficient: Since there's no figure, draw one yourself. The height to AB can be zero, so we know that AB can be the diameter of P=10, giving us an answer of 'No'. But is it always 'No'? Note that the longer the length of PC, the smaller AB grows, and vice versa. Take the figure to the other extreme  assume that PC=4. With a AP=r=5, ∆APC turns out to be recycled right triangle 3:4:5. If AC=CB=3, then AB=6. However, remember that PC<4, so AB must be slightly greater than 6. So at both extreme lengths of height PC, AB is greater than 6, and the answer is 'No', or sufficient.
_________________




Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?
[#permalink]
17 Aug 2017, 20:49






