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by B166418 » Wed Jun 29, 2011 11:19 am
If a and b are positive numbers ,what are the coordinates of the midpoint of line segment CD in XY-plane

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

A Statement 1 alone is sufficient
B Statement 2 alone is sufficient
C Both statement together are sufficient
D each statement alone is sufficient
E Statement 1 and 2 together are not sufficient
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Source: — Data Sufficiency |
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by Ashley@VeritasPrep » Wed Jun 29, 2011 2:47 pm
In order to determine the midpoint of a line segment, we will need to be able either to determine the exact endpoints of the line segment OR to determine the "average" of those points without knowing the points themselves. Information about only one of the endpoints will never be sufficient to do that, since it will leave open the possibility for the other endpoint to be absolutely anywhere, and where that other endpoint is will be super-relevant to where the midpoint falls. So (A) and (B) and (D) are all three out.

Now, if we combine the statements, it may at first appear that we still don't have sufficient information, since we can't determine the exact points C and D. BUT, to find a midpoint, we simply average the x-coordinates to get our midpoint's x-coordinate and average the y-coordinates to get our midpoint's y-coordinate. Here, when we do that, the variables a and b actually go away:

midpoint's x-coordinate = [a + (1-a)]/2 = 1/2
midpoint's y-coordinate = [(1-b) + b]/2 = 1/2

So combining the two statements takes us to the answer that the midpoint is (1/2, 1/2).
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by amit2k9 » Thu Jun 30, 2011 11:07 pm
a+b

(a+1-a)/2, (1-b+b)/2
=1/2,1/2. Hence C it is.
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