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Good DS question :

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Source: — Data Sufficiency |
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by sahilchaudhary » Sun Oct 20, 2013 9:59 am
I did a similar question in PS in GMAT Prep Test 1 (Old Version) in which the angle was 35 and radius was given 9. I also couldn't do this question at first attempt, but when I tried again, I was able to do it. This in fact uses good geometry concepts.

1. With only the radius given, there is no way to calculate length of arc CD. So, insufficient.

2. Let O be centre of circle. Join DO and CO.
Angle ACO = 30 (Since, Triangle ACO is isosceles and Angle ACO = Angle CAO and Angle CAO is given as 30)
So, Angle DCO = 60
Similarly, Angle CDO = 60
Consider Triangle OCD, using sum of angles of triangle is 180, Angle COD = 60.

Arc CD now subtends 60 degree angle, so length of arc CD is (2(pi)*r*60)/360.
But, we don't know radius 'r'. So, insufficient.

Combining 1 & 2.

Length of arc CD is (2(pi)*r*60)/360 = (2(pi)*12*60)/360 = 4(pi).

So, answer is C.

Hope this helps!
Sahil Chaudhary
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Good DS question :

by Brent@GMATPrepNow » Sun Oct 20, 2013 10:15 am
ankitbagla wrote:AB is the diameter of the circle. CD is parallel to AB. What is the length of minor arc CD?

(1) The radius of the circle is 12.

(2) The measure of ∠CAB is 30º

Image
Answer C
We can answer this question without performing any calculations. Instead, we can use some visualization.

IMPORTANT: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

This technique can save a lot of time.

Target question: What is the length of minor arc CD?

Statement 1: The radius of the circle is 12.
This information LOCKS in the size of the circle . . .
Image

. . . but it does not lock in the placement of line DC.
So, we could have something like this. . .
Image

. . . or something like this.
Image

Notice that the length of minor arc CD is different for each example.
In other words, statement 1 does not lock in the length of minor arc CD
So, statement 1 is NOT SUFFICIENT

Statement 2: The measure of ∠CAB is 30º
IMPORTANT: If we are not given ANY lengths, then we cannot find a certain length (e.g., the length of minor arc CD).
Since we are not given any lengths, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the size of the circle.
Statement 2 LOCKS in the placement of line AC (since there's only one way to draw AC such that the angle is 30º)
So, we have this.
Image

Since DC is parallel to AB, there's only one way to add DC to this diagram.
Image

So, as you can see, there's ONLY ONE WAY to draw this diagram. So, there's only one possible length of minor arc CD.
Image

Do we need to find that length? No.
We need only recognize that statements 1 and 2 combined create a situation in which there's only one possible length of minor arc CD.
As such, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 2:18 pm, edited 2 times in total.
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by ankitbagla » Sun Oct 20, 2013 10:49 am
Brent your technique is phenomenal . will apply the same in geometry ques .
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by Brent@GMATPrepNow » Sun Oct 20, 2013 11:15 am
Thanks, ankitbagla

Here's a question you can practice with: https://www.beatthegmat.com/is-there-any ... 63160.html

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Oct 20, 2013 11:22 am
Thanks, ankitbagla

Here are some questions you can practice with:
- https://www.beatthegmat.com/is-there-any ... 63160.html
- https://www.beatthegmat.com/is-there-a-s ... 63887.html
- https://www.beatthegmat.com/btg-pq-if-cd ... 85847.html

Cheers,
Brent
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by sahilchaudhary » Sun Oct 20, 2013 11:43 am
Brent@GMATPrepNow wrote:
ankitbagla wrote:AB is the diameter of the circle. CD is parallel to AB. What is the length of minor arc CD?

(1) The radius of the circle is 12.

(2) The measure of ∠CAB is 30º

Image
Answer C
We can answer this question without performing any calculations. Instead, we can use some visualization.

IMPORTANT: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

This technique can save a lot of time.

Target question: What is the length of minor arc CD?

Statement 1: The radius of the circle is 12.
This information LOCKS in the size of the circle . . .
Image

. . . but it does not lock in the placement of line DC.
So, we could have something like this. . .
Image

. . . or something like this.
Image

Notice that the length of minor arc CD is different for each example.
In other words, statement 1 does not lock in the length of minor arc CD
So, statement 1 is NOT SUFFICIENT

Statement 2: The measure of ∠CAB is 30º
IMPORTANT: If we are not given ANY lengths, then we cannot find a certain length (e.g., the length of minor arc CD).
Since we are not given any lengths, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the size of the circle.
Statement 2 LOCKS in the placement of line AC (since there's only one way to draw AC such that the angle is 30º)
So, we have this.
Image

Since DC is parallel to AB, there's only one way to add DC to this diagram.
Image

So, as you can see, there's ONLY ONE WAY to draw this diagram. So, there's only one possible length of minor arc CD.
Image

Do we need to find that length? No.
We need only recognize that statements 1 and 2 combined create a situation in which there's only one possible length of minor arc CD.
As such, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Excellent technique Brent, will try to use this when struck.
Sahil Chaudhary
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by rakeshd347 » Mon Oct 21, 2013 12:19 pm
Brent@GMATPrepNow wrote:
ankitbagla wrote:AB is the diameter of the circle. CD is parallel to AB. What is the length of minor arc CD?

(1) The radius of the circle is 12.

(2) The measure of ∠CAB is 30º

Image
Answer C
We can answer this question without performing any calculations. Instead, we can use some visualization.

IMPORTANT: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

This technique can save a lot of time.

Target question: What is the length of minor arc CD?

Statement 1: The radius of the circle is 12.
This information LOCKS in the size of the circle . . .
Image

. . . but it does not lock in the placement of line DC.
So, we could have something like this. . .
Image

. . . or something like this.
Image

Notice that the length of minor arc CD is different for each example.
In other words, statement 1 does not lock in the length of minor arc CD
So, statement 1 is NOT SUFFICIENT

Statement 2: The measure of ∠CAB is 30º
IMPORTANT: If we are not given ANY lengths, then we cannot find a certain length (e.g., the length of minor arc CD).
Since we are not given any lengths, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the size of the circle.
Statement 2 LOCKS in the placement of line AC (since there's only one way to draw AC such that the angle is 30º)
So, we have this.
Image

Since DC is parallel to AB, there's only one way to add DC to this diagram.
Image

So, as you can see, there's ONLY ONE WAY to draw this diagram. So, there's only one possible length of minor arc CD.
Image

Do we need to find that length? No.
We need only recognize that statements 1 and 2 combined create a situation in which there's only one possible length of minor arc CD.
As such, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Hi Brent,

I really love watching Gmatprepnow videos. They are not only helpful but also sometimes funny :). I wonder who have recorded them. Specially SC part is funny at times. I have seen the same problem in gmatclub but they have tried to solve it with angle properties and all.

Thanks,
Rakesh
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by Brent@GMATPrepNow » Mon Oct 21, 2013 2:15 pm
rakeshd347 wrote:
Hi Brent,

I really love watching Gmatprepnow videos. They are not only helpful but also sometimes funny :). I wonder who have recorded them. Specially SC part is funny at times. I have seen the same problem in gmatclub but they have tried to solve it with angle properties and all.

Thanks,
Rakesh
Hi Rakesh,

Thanks for the feedback. Glad to hear you like the videos. I enjoyed making them.

Cheers,
Brent
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by Gurpreet singh » Sun Jun 12, 2016 5:53 pm
Have a different approach not sure if it is right-experts can confirm.

we do not have to do any calculations

circumference of a circle is 2pir

Half of the circumference is (180/360)pir=arc ADCB

If we can find out the length of the arc AD and CD we can subtract it from arc ADCB to get CD

To find lenth of arc we need radius and inscribed angle

1. Statement 1 only radius is given. Not sufficient

2. Statement 2 angle CAB is give=30 degree. (please note this is equal to angle DCA since DC is parallel to AB)-Not sufficient.

Combing both the statements we can calculate length of respective arcs's and subtract to get CD hence answer is C.
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