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Which of the following lists the number of points at which a

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Intern
Joined: 08 Jul 2012
Posts: 10
Which of the following lists the number of points at which a  [#permalink]

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Updated on: 15 Sep 2012, 09:17
4
00:00

Difficulty:

35% (medium)

Question Stats:

58% (01:15) correct 43% (01:37) wrong based on 85 sessions

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Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8

Originally posted by Viru on 15 Sep 2012, 07:39.
Last edited by Bunuel on 15 Sep 2012, 09:17, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 22 Mar 2011
Posts: 601
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Re: Which of the following lists the number of points at which a  [#permalink]

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15 Sep 2012, 09:41
1
Viru wrote:
Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8

It is much easier to think of the intersection points between a square and a circle. Obviously, a square is a special parallelogram.

A square can intersect a circle in 8 points. See the attached drawing (leftmost figure).
There can be also 7 points of intersection, when one of the sides is tangent to the circle (middle figure). We are down to choose between D and E.
Finally, there can be only one point of intersection, when just one side is tangent to the circle (rightmost figure).
The only choice we are left with is E.

On a real test, you should not spend time to check all possible intersections.
Now, you can try to figure out all the options.
2 and 4 is easy. For 3, 5, and 6 intersection points, consider a rectangle.

Attachments

ParallelogramCircle.jpg [ 16.3 KiB | Viewed 4521 times ]

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Re: Which of the following lists the number of points at which a  [#permalink]

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15 Sep 2012, 10:51
1
Viru wrote:
Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8

Similar question to practice: which-of-the-following-lists-the-number-of-points-at-which-a-92274.html

Hope it helps.
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Re: Which of the following lists the number of points at which a  [#permalink]

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15 Sep 2012, 22:51
Thanks for the explanation, EvaJager & Bunuel
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Re: Which of the following lists the number of points at which a  [#permalink]

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01 Jul 2018, 05:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following lists the number of points at which a &nbs [#permalink] 01 Jul 2018, 05:36
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