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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.

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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03 Jul 2016, 02:39

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

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29 Aug 2017, 09:05

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

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

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29 Aug 2017, 12:30

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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