Question 161435: Points R, J, S, G are collinear. If RJ=SG and RJ, JS, and SG are integaers, what value is NOT possible for RG if JS= 15?
A: 18
B: 21
C: 25
D: 17
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the order of the points are R, J, S, G
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! order of points is RJSG (given)
RG is the whole line which is composed of the parts RJ, JS, and SG. (given)
JS = 15 (given)
RJ = SG (given)
RJ, JS, and SG are integers (given).
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RG = RJ + JS + SG (sum of the parts equals the whole).
RG = RJ + 15 + SG (substitution since JS = 15)
RG = 15 + 2*RJ (since RJ = SG, then we can susbsitute RJ for SG).
subtract 15 from both sides of equation.
RG - 15 = 2*RJ
divide both sides of equation by 2.
(RG - 15)/2 = RJ
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since RJ must an integer, then the equation on the left must also be an integer.
choices are:
18, 21, 25, 17
(18 - 13)/2 = 3/2 = 1.5 no good
(21 - 15)/2 = 6/2 = 3 ok
(25 - 15)/2 = 10/2 = 5 ok
(17 - 15)/2 = 2/2 = 1 ok
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answer is A (18).
RG cannot be 18 because (18-15)/2 equals 3/2 = 1.5 which is not an integer.
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answer is A.
JS cannot be equal to 1.5.
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