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Math Expert V
Joined: 02 Sep 2009
Posts: 58437
A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:14) correct 26% (01:10) wrong based on 167 sessions

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A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
(2) The y-intercept of the straight line is 6.

_________________

Originally posted by Bunuel on 01 Jul 2016, 04:24.
Last edited by Vyshak on 01 Jul 2016, 09:17, edited 1 time in total.
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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
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Location: India
Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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St1: Insufficient as we do not know the equation of the straight line

St2: Insufficient as we do not know the equation of the circle or the straight line

Combining St1 and St2: Still insufficient as we only the equation of the circle

Senior Manager  Joined: 23 Apr 2015
Posts: 285
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Answer is E: Neither is sufficient to solve.

(1) The equation of the circle is x^2 + y^2 = 25.
This says this is a circle of radius 5 and centre as origin and nothing about the line. So Eliminate A and D

(2) The y-intercept of the straight line is 6.
This says about the line with y intercept as 6, but not about the slope, so incomplete line information and also nothing about the Circle.

combining 1 and 2 , we know about a circle and an incomplete line, so E.
Senior Manager  Joined: 02 Mar 2012
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Schools: Schulich '16
Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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E

taking both and had the slope been given it was suff,
Manager  Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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hsbinfy wrote:
E

taking both and had the slope been given it was suff,

Hi hsbinfy,

I understand that both statements are insufficient and the answer to this problem is E. However, can you please explain how would slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle
Manager  Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Hello experts,

Can you please confirm my understanding?

I agree that the answer to this problem is E. However, can you please explain if slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle

Thank you.
Math Expert V
Joined: 02 Sep 2009
Posts: 58437
Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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1
Donnie84 wrote:
Hello experts,

Can you please confirm my understanding?

I agree that the answer to this problem is E. However, can you please explain if slope help us here? If the slope was given, how can we tell how many places the line would intersect? Maybe I'm overthinking but can we not have two cases even if slope was given:

1. Line is tangent to the circle
2. Line is secant to the circle

Thank you.

A point and the slope defines a line. So, we would be able to get the equation of the line and answer the question.

Check for more here: math-coordinate-geometry-87652.html
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Manager  Joined: 04 Jan 2014
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GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Thanks Bunuel. It is clear now.
Director  B
Joined: 04 Jun 2016
Posts: 556
GMAT 1: 750 Q49 V43 Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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Bunuel wrote:
A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
(2) The y-intercept of the straight line is 6.

A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

(1) The equation of the circle is x^2 + y^2 = 25.
The origin of the circle is at (0,0) and has a radius of 5.
We don't know anything about the line
INSUFFICIENT

(2) The y-intercept of the straight line is 6.
No information about the circle
INSUFFICIENT

Merging both statement
A circle of radios 5 is drawn a the origin and a line with Y intercept at 6 is drawn. The line has one xy pair as (0,6). what about the slope or other (X,Y) pair.
We don't know if the line is horizontal (Won't meet the circle), vertical (meet the circle at two points) or inclined (might meet the circle at 2 points , one points or no points at all)

INSUFFICIENT.

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Re: A circle and a straight line are drawn on the same coordinate graph.  [#permalink]

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_________________ Re: A circle and a straight line are drawn on the same coordinate graph.   [#permalink] 23 Jan 2018, 06:35
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