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A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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Question Stats: 59% (01:39) correct 41% (01:46) wrong based on 323 sessions

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A circle is drawn in the xy-coordinate plane. If there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are:

a) 0, 1, or 2

b) 0, 2, or 4

c) 0 or 4

d) 0, 2, 3, or 4

e) 0, 1, 2, 3, or 4
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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Given: xy = 0 --> xy is a line on the x axis or y axis
We have to find the number of points of intersection of xy with the circle.

As seen in the attached figure, answer is E.
Attachments IMG_20151230_212028.jpg [ 1.05 MiB | Viewed 7202 times ]

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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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When Circle is not touching any of the X axis or Y axis, how the condition xy=0 is satisfied ?
could you please explain.
thanks for your help
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kannu44 wrote:
When Circle is not touching any of the X axis or Y axis, how the condition xy=0 is satisfied ?
could you please explain.
thanks for your help

This is the case when the condition is not satisfied, so when the answer is that there are 0 points (x, y) on the circle such that xy = 0.
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For n = 4, how is the condition x*y = 0 satisfied ?? In the figure attached, neither x nor y is 0 for n = 4 ! So how is the case satisfied ??
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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dflorez wrote:
A circle is drawn in the xy-coordinate plane. If there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are:

a) 0, 1, or 2

b) 0, 2, or 4

c) 0 or 4

d) 0, 2, 3, or 4

e) 0, 1, 2, 3, or 4

Bunuel could u pls explain what is this question asking for? kind of ambiguous for me
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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Bunuel chetan2u niks18

Quote:
A circle is drawn in the xy-coordinate plane.

Is not this kind of an universal truth? A circle is a 2D figure.
What do I infer from this sentence?

Quote:
If there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are:

How do I make sure: (x,y) refer to circumference and not area?
Can I infer we are talking about intercepts from (x,y) = 0?
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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Quote:
A circle is drawn in the xy-coordinate plane.

Is not this kind of an universal truth? A circle is a 2D figure.
What do I infer from this sentence?
Yes it is a 2D figure. but it could be xz or yz although we normally talk of xy coordinates... so its OK as we are dealing with x,y thereafter

Quote:
If there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are:

How do I make sure: (x,y) refer to circumference and not area?
Can I infer we are talking about intercepts from (x,y) = 0?
Since it is given ON the circle, it is talking of (x,y) lying on the circumference..
Had it been IN the circle, we would have talked about area

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A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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chetan2u

Quote:
Yes it is a 2D figure. but it could be xz or yz although we normally talk of xy coordinates... so its OK as we are dealing with x,y thereafter

What is z in in your reply?

Ideally a single point on / inside the circle will still be represented only by an order pair (x,y)

This not a sphere Q, representing (x,y,z) . Why is at all is first sentence required to be given?
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chetan2u

Quote:
Yes it is a 2D figure. but it could be xz or yz although we normally talk of xy coordinates... so its OK as we are dealing with x,y thereafter

What is z in in your reply?

Ideally a single point on / inside the circle will still be represented only by an order pair (x,y)

This not a sphere Q, representing (x,y,z) . Why is at all is first sentence required to be given?

what if I draw it on ground or on wall... both are different planes..

But as I told you , you dont have to worry about it. But mentioning a circle in xy-coordinate is perfectly fine
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A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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xy plane can be written as (x,y,0).
z = 0 for xy plane. similarly xz plane would be (x,0,z) ,y will be zero in xz plane. It is possible to have equation of circle as $$x^2+z^2=16$$ in xz plane

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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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But as the question explicitly states points (x,y) lies on circle, hence it is in xy plane.

There is no point in contemplating about different other planes possible.

Princ wrote:
xy plane can be written as (x,y,0).
z = 0 for xy plane. similarly xz plane would be (x,0,z) ,y will be zero in xz plane. It is possible to have equation of circle as $$x^2+z^2=16$$ in xz plane

Sent from my XT1068 using GMAT Club Forum mobile app

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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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Math experts can you please help explain this? as in visually???
Since xy=0, i do understand that either x or y or both can be 0. But how do i assume different points on the xy coordinate?
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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VQ

Question ask us to find the possible value of n where xy=0

It means we need to find the case when points on the circle can have value as xy = 0 (i.e. Minimum to maximum values)

as explained by Vyshak visually , n can take value from 0 to 4

Hope it helps _________________
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A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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soapbolt wrote:
VQ

Question ask us to find the possible value of n where xy=0

It means we need to find the case when points on the circle can have value as xy = 0 (i.e. Minimum to maximum values)

as explained by Vyshak visually , n can take value from 0 to 4

Hope it helps Lets say if this question had an option of 7-8 integers starting from 0-7 (same as E)..
That would have been our answer in that case ?

Main point to note is that : It must contain a 0 and all other maximum possible points, right. ?
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Re: A circle is drawn in the xy-coordinate plane. If there are n differen  [#permalink]

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vrindachopra wrote:
For n = 4, how is the condition x*y = 0 satisfied ?? In the figure attached, neither x nor y is 0 for n = 4 ! So how is the case satisfied ??

In the figure, the largest circle is the case with 4 points.
When the circle crosses any of the points on the axis either x=0 or y=0 and hence xy=0 Re: A circle is drawn in the xy-coordinate plane. If there are n differen   [#permalink] 25 Apr 2019, 07:51
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