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M13-25

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M13-25  [#permalink]

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New post 15 Sep 2014, 23:49
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (01:16) correct 69% (01:46) wrong based on 98 sessions

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Points \(A\), \(B\), \(C\) and \(D\) lie on a circle of radius 1. If \(x\) is the length of arc \(AB\) and \(y\) the length of arc \(CD\) respectively, such that \(x \lt \pi\) and \(y \lt \pi\), is \(x \gt y\)?


(1) \(\angle ADB\) is acute

(2) \(\angle ADB \gt \angle CAD\)

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Re M13-25  [#permalink]

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New post 15 Sep 2014, 23:49
1
3
Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. These angles seem to define the lengths of arcs. The angles can come from different sides of the arc. On the images below you can see that both cases comply with the S2, but have different answers to the question. We need one more condition to define the arcs.

Image Image

Statements (1) and (2) combined are sufficient. If \(\angle\) ADB is acute and greater than \(\angle\) CAD, then arc \(AB\) is greater than arc \(CD\).


Answer: C
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Re: M13-25  [#permalink]

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New post 12 Sep 2015, 23:24
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. These angles seem to define the lengths of arcs. The angles can come from different sides of the arc. On the images below you can see that both cases comply with the S2, but have different answers to the question. We need one more condition to define the arcs.

Image Image

Statements (1) and (2) combined are sufficient. If \(\angle\) ADB is acute and greater than \(\angle\) CAD, then arc \(AB\) is greater than arc \(CD\).

Answer: C



Choice B is very tempting !!
I got it wrong :(
But, thanks for the explanation.
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Re: M13-25  [#permalink]

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New post 26 Jan 2016, 23:03
Statements (1) and (2) combined are sufficient. If ∠ ADB is acute and greater than ∠ CAD, then arc AB is greater than arc CD.

Can you elaborate on this?
Also where do we use the fact that both arcs are < pi?
I feel like this has some very complicated geometry involved. :S
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Re: M13-25  [#permalink]

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New post 06 Aug 2016, 05:01
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. These angles seem to define the lengths of arcs. The angles can come from different sides of the arc. On the images below you can see that both cases comply with the S2, but have different answers to the question. We need one more condition to define the arcs.

Image Image

Statements (1) and (2) combined are sufficient. If \(\angle\) ADB is acute and greater than \(\angle\) CAD, then arc \(AB\) is greater than arc \(CD\).


Answer: C





Hi Bunuel,

Can you please explain how combining both statements will help in taking a decision that AB>CD ?
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Re: M13-25  [#permalink]

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New post 06 Aug 2016, 10:04
avdgmat4777 wrote:
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. These angles seem to define the lengths of arcs. The angles can come from different sides of the arc. On the images below you can see that both cases comply with the S2, but have different answers to the question. We need one more condition to define the arcs.

Image Image

Statements (1) and (2) combined are sufficient. If \(\angle\) ADB is acute and greater than \(\angle\) CAD, then arc \(AB\) is greater than arc \(CD\).


Answer: C





Hi Bunuel,

Can you please explain how combining both statements will help in taking a decision that AB>CD ?


Check here: points-a-b-c-and-d-lie-on-a-circle-of-radius-1-let-x-be-69615.html
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Collection of Questions:
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Re: M13-25  [#permalink]

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New post 17 Aug 2016, 00:50
Hi Bunuel,

Since x and y both are arcs and less than pie, and as radius is 1, hence both the arcs are less than a semi circle. Now combining this with ∠ADB>∠CAD, it means both are acute angles, because these could have been 90 degree if they would have been making a semicircle arc or larger if the arc would have been larger, but neither is the case. Hence the answer should be B.

Am I thinking right or missing something?
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Re: M13-25  [#permalink]

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New post 17 Aug 2016, 01:05
bjain01 wrote:
Hi Bunuel,

Since x and y both are arcs and less than pie, and as radius is 1, hence both the arcs are less than a semi circle. Now combining this with ∠ADB>∠CAD, it means both are acute angles, because these could have been 90 degree if they would have been making a semicircle arc or larger if the arc would have been larger, but neither is the case. Hence the answer should be B.

Am I thinking right or missing something?


Check here: points-a-b-c-and-d-lie-on-a-circle-of-radius-1-let-x-be-69615.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M13-25  [#permalink]

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New post 16 Jul 2018, 03:05
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. These angles seem to define the lengths of arcs. The angles can come from different sides of the arc. On the images below you can see that both cases comply with the S2, but have different answers to the question. We need one more condition to define the arcs.

Image Image

Statements (1) and (2) combined are sufficient. If \(\angle\) ADB is acute and greater than \(\angle\) CAD, then arc \(AB\) is greater than arc \(CD\).


Answer: C

Hi BUnuel,
One doubt here how can we measure ADB whether it is obtuse or acute is there any property in circle.
Especially in above two figures how the angle difference is spotted?
Pls explain
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Re: M13-25  [#permalink]

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New post 22 Oct 2018, 03:21
82vkgmat wrote:
Statements (1) and (2) combined are sufficient. If ∠ ADB is acute and greater than ∠ CAD, then arc AB is greater than arc CD.

Can you elaborate on this?
Also where do we use the fact that both arcs are < pi?
I feel like this has some very complicated geometry involved. :S


I think the fact that both arcs are < pi is mentioned cuz we are suppose to consider only the minor arcs (less than half the perimeter) of the 2 points and not the major arcs.

The reason it is vital is because the result of comparing minor arcs of 2 sets of points would be opposite of comparing the result of 2 major arcs of the same set of points.
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Re: M13-25 &nbs [#permalink] 22 Oct 2018, 03:21
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