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

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

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14 Sep 2016, 06:13
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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.

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

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

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

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

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

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

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

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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 ]

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

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

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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 ]

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

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

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

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

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14 Sep 2016, 21:22
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
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Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?  [#permalink]

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

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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 hereAB = 2*2.9 = 5.8 and it is <6

2)X = 3.1,AB = 3.9, R = 5 we can form a triangle so hereAB = 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
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Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?  [#permalink]

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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 hereAB = 2*2.9 = 5.8 and it is <6

2)X = 3.1,AB = 3.9, R = 5 we can form a triangle so hereAB = 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
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Re: P is a circle with radius r. If AB is a chord in circle P, is AB<6?  [#permalink]

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

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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.

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

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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->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.
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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
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