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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Aug 13, 2013 8:57 pm

A circle with diameter 10 is centered on the origin. Which of the following points are on the circle?

a) 5,0
b) 5,5
c) -3, 4
d) 1, -2(sqroot6)
e) -2, 2(sqroot6)

OA is a,c,d

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Source: Beat The GMAT — Problem Solving | Tue Aug 13, 2013 8:57 pm

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Tue Aug 13, 2013 9:11 pm

sana.noor wrote:A circle with diameter 10 is centered on the origin. Which of the following points are on the circle?

a) 5,0
b) 5,5
c) -3, 4
d) 1, -2(sqroot6)
e) -2, 2(sqroot6)

OA is a,c,d

Diameter = 10
Radius = 5
All the points which have distance from the origin = 5 lie on the circle.
In this case, a,c, and d

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Tue Aug 13, 2013 9:18 pm

the essence is that the digonal must be 5 in order to be it on circle if the any of the two vertices is not zero

for d = {{-2(6)^1/2}^2} + (1)]^2 = (25)^1/2 = 5
a nd c are clearly on circle

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Aug 13, 2013 9:24 pm

i understand the question but need reasoning behind the answer choices so starters can understand this issue
b) 5,5 cannot be the point on the circle because when x = 5 y will be zero and as we start decreasing the value of x the value of y increases. when y = 5 then x= 0. thus no such point can exist on the circle.
e) 2(sqroot6) is nearly equals to 5 (4.89). if we draw the diagram we can understand that when x=-2 the value of y will lie outside the circle.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Aug 13, 2013 9:45 pm

Hi sana.noor,

To help you solve this problem, try drawing a circle as the question describes it (on a graph, around the origin, with a diameter of 10, so the radius is 5).

Since the radius is 5, and you're looking for points that are on the circumference of the circle, you can use the Pythagorean Theorem to figure out which points are on the circumference and which ones are not.

For example, with Answer C (-3,4):
1) Graph that point and then draw a line from the origin (0,0) to (-3,4).
2) Notice that it's a diagonal line? You should be able to draw a RIGHT TRIANGLE, using that diagonal line as the hypotenuse.
3) Now, using the values of THAT point, see if Pythagorean Thm balances: A^2 + B^2 = C^2
4) Does (-3)^2 + (4)^2 = 5^2????
5) It DOES!!! So, THAT point is on the circumference.

6) Now try the other points.

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Sat Aug 17, 2013 6:31 am

A multiple-choice problem with 3 correct answers? Huh? Where'd you get this?
Hopefully not from a GMAT source...

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Sun Aug 18, 2013 8:47 pm

Ron its from Veritas

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