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Is the radius of circle Q longer than 2?

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Is the radius of circle Q longer than 2? [#permalink]

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New post Updated on: 06 Jun 2015, 10:49
2
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (00:50) correct 45% (01:08) wrong based on 139 sessions

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Is the radius of circle Q longer than 2?

(1) The circumference of circle Q is longer than 12.
(2) AB is a chord of length 5 in circle Q.

SOLUTION:
To understand Stat.(1), employ the circumference formula = 2πr>12. Solve for r and simplify to get r>6/π. π is greater than 3, so the right side of this inequality is equal to less than 2, (ballpark it at ~1.9.) So if the circumference is 12.1, r is smaller than 2 but longer than ~1.9, giving an answer of 'no'. However, is this always true? for any number? If the circumference is 1000, then r is equal to 500/π - much greater than 2, giving an answer of 'yes. Therefore, Stat.(1)->Maybe->IS->BCE.

Since the diameter is the longest possible chord in a circle, Stat.(2) really means the diameter is longer than, or equal to 5. This means that the radius ≥ than 2.5, and thus greater than 2. Hence, Stat.(2)->Yes->S->B.

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Originally posted by reto on 06 Jun 2015, 04:29.
Last edited by Bunuel on 06 Jun 2015, 10:49, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is the radius of circle Q longer than 2? [#permalink]

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New post 06 Jun 2015, 13:55
1
2
This question is pretty easily solved with some quick mental math and basic knowledge of circles.

Is the radius of circle Q longer than 2?
We are not given much information here, so we head to the statements focusing on radius.

(1) The circumference of circle Q is longer than 12.
C = 2*pie*r. Pie is 3.14. So 6.28*r is greater than 12. R could be less than, equal to, or longer than 2. Insufficient.

(2) AB is a chord of length 5 in circle Q.
The longest chord of a circle is its diameter. If the diameter is 5, then the radius would be 2.5. If this chord is not the diameter, then the diameter is even longer and the radius bigger than 2.5. Either way, we have a definitive "yes" to the question, thus this is sufficient.

Answer choice B, statement 1 not sufficient and statement 2 sufficient. I hope this helps!
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Re: Is the radius of circle Q longer than 2? [#permalink]

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New post 29 Aug 2017, 10:18
reto wrote:
Is the radius of circle Q longer than 2?

(1) The circumference of circle Q is longer than 12.
(2) AB is a chord of length 5 in circle Q.

SOLUTION:
To understand Stat.(1), employ the circumference formula = 2πr>12. Solve for r and simplify to get r>6/π. π is greater than 3, so the right side of this inequality is equal to less than 2, (ballpark it at ~1.9.) So if the circumference is 12.1, r is smaller than 2 but longer than ~1.9, giving an answer of 'no'. However, is this always true? for any number? If the circumference is 1000, then r is equal to 500/π - much greater than 2, giving an answer of 'yes. Therefore, Stat.(1)->Maybe->IS->BCE.

Since the diameter is the longest possible chord in a circle, Stat.(2) really means the diameter is longer than, or equal to 5. This means that the radius ≥ than 2.5, and thus greater than 2. Hence, Stat.(2)->Yes->S->B.


Similar question to practice: https://gmatclub.com/forum/is-the-radiu ... 28698.html
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Re: Is the radius of circle Q longer than 2? [#permalink]

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New post 29 Aug 2017, 12:23
Find if radius is > 2


1) circumference is greater than 12:
2*pi*r >12
r> 6/pi ie r> 6/ (22/7) ie r> 21/11

So r> 1.9

But we cannot say if r is greater than 2 as r>1.9 can imply r=1.91 or r=2 or r=4 anything

Insufficient


2) Given cord length is 5.
Assume given cord is diameter ( as longest cord in a circle is diameter) . So radium = diameter/2 => r=2.5

So even considering given cord to be longest r=2.5 . So in given condition r >=2.5 Always.

Sufficient


Answer : B
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Re: Is the radius of circle Q longer than 2? [#permalink]

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New post 29 Aug 2017, 13:30
1) 2x 3.14 xR > 12
R> 1. something
R can be 1.99 and can be 2.01. AD ruled out insufficient.
2) chord of length 5 is in circle, any chord will be max if its diameter , let it be a diameter then radius is 2.5
if this chord is anywhere else in circle then more than its length will be diameter which says R>=2.5
definitely yes R>2 there fore B is our answer
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Re: Is the radius of circle Q longer than 2?   [#permalink] 29 Aug 2017, 13:30
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