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A square and a circle intersect at more than one point. Does the squa

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A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 11 Mar 2015, 03:50
2
3
00:00
A
B
C
D
E

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A square and a circle intersect at more than one point. Does the square have more area than the circle?

(1) there are exactly four intersection points
(2) at least two of the intersection points are on vertices of the square

Kudos for a correct solution.

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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 11 Mar 2015, 06:01
2
Hi

Statement i
circle can be outside or inside




Statement ii
Can not answer with it as circle can be outside on either side
cannot say the position can be as shown in the pic below

i + ii still not sufficient

Correct me if i am wrong..!!
Attachments

cir2.png
cir2.png [ 15.47 KiB | Viewed 2971 times ]


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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 11 Mar 2015, 06:30
the answer is E

from statment 1 is insuff because the circle is either smaller or larger which mean the circle could be inside or outside the square

from statment 1 is insuff because the circle is either smaller or larger which mean the circle could be inside or outside the square

or could be just half of the circle inside or out side the square

statment 1&2 the circle is intersects the square in four vertices and the circle could be larger or smaller the square so both statment are insuff
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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 11 Mar 2015, 06:45
'C' . The only conceivable figure in which this fits is the Circle enveloping the Square.


But of course , it can't be that easy, so . :P
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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 15 Mar 2015, 21:46
Bunuel wrote:
A square and a circle intersect at more than one point. Does the square have more area than the circle?

(1) there are exactly four intersection points
(2) at least two of the intersection points are on vertices of the square

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Statement #1: this information, with nothing more, could mean that the circle is either smaller or larger.
Attachment:
cpotg_img20.png
cpotg_img20.png [ 11.21 KiB | Viewed 2820 times ]

This statement, alone and by itself, is insufficient.

Statement #2: this information, with nothing more, could mean that the circle is either smaller or larger.
Attachment:
cpotg_img21.png
cpotg_img21.png [ 13.37 KiB | Viewed 2808 times ]

This statement, alone and by itself, is insufficient.

Combined Statements: One possibility is the circle that intersects the square four times by passing through all four vertices:
Attachment:
cpotg_img22.png
cpotg_img22.png [ 6.07 KiB | Viewed 2806 times ]

That circle is clearly bigger than the square. The circle absolutely cannot pass through exactly three vertices. If it pass through two vertices, it would have to intersect the side two more times. Possibilities include the following (point C is the center of the circle).
Attachment:
cpotg_img23.png
cpotg_img23.png [ 15.47 KiB | Viewed 2808 times ]


Notice that, as point C approaches the top side of the square, it gets closer and closer to the circle that has this top side as a diameter, equivalent to the first circle in the statement #1 diagram. That circle is clearly has less area than the square. Well, that circle won’t work here, because it intersects at only two points, but because point C could get closer and closer to the top side without touching it, which means the area of the circle in this diagram could get closer and closer to the area of the first circle in the statement #1 diagram. This means that we could make the circle in this diagram have less area than the square has.
Thus, even with the constraints of both statements, we can construct a circle that has an area that is either greater than or less than that of the square. Even with both statements, we cannot give a definitive answer to the prompt question.

Both statements combined are insufficient.
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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: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 17 Nov 2015, 18:23
indeed, a tricky one...
one might consider statement 2 alone as sufficient to say that the square is circumscribed and thus circle has a greater area but!!! in the question it is specified that there are at least 1 point of intersection. There might be 2 points of intersection, 3, 4, 5, 6 etc.

E is the correct answer.
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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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New post 31 Jul 2016, 11:31
Bunuel wrote:
A square and a circle intersect at more than one point. Does the square have more area than the circle?

(1) there are exactly four intersection points
(2) at least two of the intersection points are on vertices of the square

Kudos for a correct solution.

Please refer the attached for consideration
neither option suff...
Ans E
Attachments

Untitled.png
Untitled.png [ 8.16 KiB | Viewed 1980 times ]

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Re: A square and a circle intersect at more than one point. Does the squa  [#permalink]

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Re: A square and a circle intersect at more than one point. Does the squa &nbs [#permalink] 09 Jul 2018, 09:28
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