collection of tough problems from G PREP - 15 - The Beat The GMAT Forum

collection of tough problems from G PREP - 15

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Sat Feb 06, 2010 5:32 am

Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1

(2) The slope of line K is -1/10

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Source: Beat The GMAT — Data Sufficiency | Sat Feb 06, 2010 5:32 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Sat Feb 06, 2010 6:16 am

abhasjha wrote:Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1

(2) The slope of line K is -1/10

Basic rule 1:A line can intersect at maximum 2 points.
Basic rule 2:A unique line equation can be found by knowing 2 variables(the slope and the intercept)

Hence,C.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 06, 2010 8:29 am

abhasjha wrote:Circle C and line K lie in the xy plane. If circle C is centered at the origin and has radius 1 , does line K intersect circle C??

(1) The x intercept of line k is greater than 1

(2) The slope of line K is -1/10

1.) The x intercept of line k is greater than 1; x intercept is greater than one but this doesnt assure the line intersects the circle or not

2) slope is -1/10 is insufficient to conclude whether the line intersects the circle

combining 1&2 we can derive the equation of the line and check whether the circle is intersected by the line

Always borrow money from a pessimist, he doesn't expect to be paid back.

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Mon Feb 08, 2010 12:28 am

OA - E

just draw a circle with the center at 0,0... with a radius of 1 the circle will touch (0,1) (1,0) (0,-1) & (-1,0)

Statement (1) tells you that line K (and i'm pretty sure that yes you imagine it's infinite because it would be called line segment k something not line k) has an x-intercept greater than 1... on your diagram this would be to the right of the point (1,0) you have the circle touching... since you have no idea how far right this point is, it could be at (5000,0) or (2,0) and you have no idea what the slope is, it could be a vertical line like x=5000 or x=2 and never touch the circle, or a regular positive or negative slope. Not sufficient

Statement (2) tells you that the slope of line k is -1/10... this tells you absolutley nothing about the placement of the line in relation of the circle... not sufficient

Together imagine the two examples I gave for possible places of line k on the x-axis... If line K's x-intercept was at (2,0) with a slope of -1/10 it would run right into the circle as it is 1 unit away and hit the y-axis at (0,1/5) (in the circle)... now imagine the line K hits the x-axis at (5000,0) all the way to the right of the circle with a slope of -1/10 it would run all the way back to the y-axis and touch it at (0,500) way above the circle...

therefore the answer is E

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