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555-605 (Medium)|   Geometry|      
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rohan2345
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Which of the following could be both within a square with radius of 1? 29 Jul 2019, 07:52
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

64% (01:26) correct 36% (01:38) wrong based on 85 sessions

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Which of the following could be both within a square with radius of 1?

(A) (1,1) and (2,3)

(B) (-2,-1) and (1, 2)

(C) (4, 6) and (5, 5)

(D) (-5,-6) and (-7, -8)

(E) (-3,0) and (0,-4)
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C
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TheNightKing
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GMAT 1: 600 Q46 V27
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Which of the following could be both within a square with radius of 1? 03 Aug 2019, 13:21
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rohan2345
Which of the following could be both within a square with radius of 1?

(A) (1,1) and (2,3)

(B) (-2,-1) and (1, 2)

(C) (4, 6) and (5, 5)

(D) (-5,-6) and (-7, -8)

(E) (-3,0) and (0,-4)
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May be a weird approach. If the circle to be at the Center (0,0) I can only travel a distance of 1 unit from each side since the radius is 1.
Only C allows me to the do that.

I can be wrong on this one. Please correct me if I am
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Which of the following could be both within a square with radius of 1? 03 Aug 2019, 14:05
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If the two points are in a circle with a radius of 1 unit, then the distance between them should not exceed the diameter, which is 2 units here.

So only option C satisfies that criteria where the distance between both the points is less than 2

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stne
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Which of the following could be both within a square with radius of 1? 28 Sep 2021, 07:35
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rohan2345
Which of the following could be both within a square with radius of 1?

(A) (1,1) and (2,3)

(B) (-2,-1) and (1, 2)

(C) (4, 6) and (5, 5)

(D) (-5,-6) and (-7, -8)

(E) (-3,0) and (0,-4)
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A square cannot have a radius, it can only have a side and a diagonal.

Assuming the question means to say, that the " Radius of a circle inscribed in a square is 1 cms " then which of the following two points could be within the square?

If the radius of the inscribed circle is \(1\) cms then the square is of side \(2\) cms and the longest distance within the square is \(2\sqrt{2}\). So the distance within the two points should be less than \(2\sqrt{2}\) to fulfill the criteria.

IF the distance between the two points is more than \(2\sqrt{2}\) then both the points cannot be inside the square.

(A) (1,1) and (2,3) -> \(\sqrt{5} > 2\sqrt{2}\)

(B) (-2,-1) and (1, 2) ->\(3\sqrt{2}> 2\sqrt{2}\)

(C) (4, 6) and (5, 5) -> \(\sqrt{2} < 2\sqrt{2}\)

(D) (-5,-6) and (-7, -8) -> \(2\sqrt{2} = 2\sqrt{2}\)

(E) (-3,0) and (0,-4) -> \(5 > 2\sqrt{2}\)

Since we are asked within the square , choice C is the best option.

Attachment:
Gmat square.png
Gmat square.png [ 4.36 KiB | Viewed 1128 times ]

Ans C

Hope it's clear.
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