Points on a graph

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Rastis: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Sep 21, 2011 7:06 amFollowed by: 2 members; Location: Washington, DC; Thanked: 6 times; GMAT Score:500

by Rastis » Mon Dec 08, 2014 12:45 pm

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

a) The coordinates of C are (a, 1-b)

b) The coordinates of D are (1-a, b)

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 08, 2014 12:45 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Dec 08, 2014 12:55 pm

If a and b are positive numbers , what are the coordinates of the midpoint of the line segment CD in the xy-plane ?

1) The coordinates of C are ( a , 1-b)

2) The coordinates of D are ( 1-a, b)

Target question: What are the co-ordinates of midpoint of segment CD

If we have two points (x1 , y1) and (x2, y2), then the midpoint of this points will be [(x1 + x2)/2 , (y1 + y2)/2]

In other words, to find the midpoint, we find the average of the x-coordinates and the average of the y-coordinates.

Statement 1: co-ordinates of C are (a, 1-b)
Since we have no information about point D, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: co-ordinates of D are (1-a, b)
Since we have no information about point C, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We have C(a,1-b) and D(1-a,b), so the midpoint is [(a + 1-a)/2 , (1-b + b)/2]
When we simplify, we get (1/2 , 1/2)
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Dec 08, 2014 12:56 pm

Rastis wrote:If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

a) The coordinates of C are (a, 1-b)

b) The coordinates of D are (1-a, b)

The midpoint between two points is the average of the x-coordinates and the average of the y-coordinates:
midpoint = [ (xâ‚� + xâ‚‚)/2, (yâ‚� + yâ‚‚)/2 ].

Clearly, neither statement alone is sufficient.
Statements combined:
midpoint = [ (a + 1-a)/2 , (1-b + b)/2 ] = (1/2, 1/2).
SUFFICIENT.

The correct answer is C.

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