Solve GRE Geometry Problem: X-Y = 30

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The discussion revolves around a GRE geometry problem involving two variables, X and Y, where the objective is to determine the value of X-Y. The problem presents two equations: 2X + 2Y = 180 and 2X + Y + 30 = 180. The correct solution indicates that X-Y equals 30, although the initial poster expresses confusion about how this conclusion was reached. By solving the two equations for X and Y, the values can be computed to find X-Y. The thread emphasizes the importance of algebraic manipulation in solving geometry problems.
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I've attached an MS paint version of a GRE geometry problem. It's a quantitative comparison question. It asks you to compare two values and say whether one is greater, they're the same, or they're not enough information to say which is greater.

In the picture I drew everything is in degrees. It's not necessarily to scale.

As I've said in the picture, the actual answer is that (X-Y) is equal to the value 30. I have no clue how they figured this out though I would've said not enough information to answer.
 

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    GRE Geometry Problem.GIF
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Notice that 2X+2Y=180 and that 2X+Y+30=180.

Two equations, two unknows, solve for X and Y, then compute X-Y.
 
Brilliant. thank you.
 

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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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