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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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, 06:32

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

P is a circle with radius r. If AB is a chord in circle P, is AB<6? [#permalink]

Show Tags

14 Sep 2016, 06:45

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.

Last edited by msk0657 on 14 Sep 2016, 11:02, edited 2 times in total.

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, 08:00

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.

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, 10:10

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..

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, 10:23

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?

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, 10:28

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?

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, 10:32

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?

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, 11:02

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..

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, 20:22

C.

If height equals to 4, then half of the chord equals to 3 (25-16=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
_________________

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, 14:35

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.

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, 19:49

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->IS-CE

(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.
_________________