If the length of arc ACB in the circle above is 5p, is the length of A

Question

https://gmatclub.com/forum/download/file.php?id=58433 If the length of arc ACB in the circle above is 5\pi , is the length of AB greater than the length of CD ? (1) The length of AB equals the circle’s diameter. (2) The length of CD is 5. 2020-10-17_23-25-04.png

Mona2019 · Answer

The greatest chord in a circle is the diameter. But both AB and CD can be equal too.
So we can't say A is sufficient

B gives the length of CD , but how is this length related to 5p,
Insufficient

Together they are insufficient too. As we don't know CD's length .

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TestPrepUnlimited · Answer

Note AB and CD are not necessarily chords that go through the center of the circle. (Usually the question would state AB and CD are simply chords).

Statement 1: 
We don't know if AB is greater than CD or equal to CD so insufficient. We also know the radius is  \frac{2*5*\pi }{ (2*\pi)}  = 5, and AB = 5*2 = 10.

Statement 2: 
Need to know AB, insufficient.

Combined: 
Now we know AB > CD so sufficient.

Ans: C

Mona2019 · Answer

TestPrepUnlimited 
How do we know 5p is same as 5π?

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vigneshvnair · Answer

Clause A reveals that 2 * 5p = 10p is the perimeter and that diameter AB = 10p/pi, but I don’t understand how the leap was made to replace p with pi. Can someone explain this to me?

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swati1351 · Answer

Yeah, I faced the same issue too. After crossing out both the options and considering 'E', I thought to myself, only if this given length was 5 pi, the answer could be C. It's definitely confusing.

vigneshvnair · Answer

I eventually selected E because logically I had run out of options. I suppose one can’t always “IS” one’s way through every choice 🤷🏽‍♂️ I certainly hope that the OA is reviewed soon because this might throw off some well-prepared prospective test-takers.

stne · Answer

Bunuel ,

May be p should be replaced with  \pi  in this question?

Bunuel · Answer

Good catch. Yes, you are right. Edited. Thank you.

If the length of arc ACB in the circle above is 5p, is the length of A

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