MathDB

16

Part of 2015 AMC 10

Problems(2)

Symmetric Algebraic Equation

Source: 2015 amc 10a #16

2/4/2015
If y+4=(x−2)2,x+4=(y−2)2y+4 = (x-2)^2, x+4 = (y-2)^2, and x≠yx \neq y, what is the value of x2+y2x^2+y^2?
<spanclass=′latex−bold′>(A)</span>10<spanclass=′latex−bold′>(B)</span>15<spanclass=′latex−bold′>(C)</span>20<spanclass=′latex−bold′>(D)</span>25<spanclass=′latex−bold′>(E)</span>30 <span class='latex-bold'>(A) </span>10\qquad<span class='latex-bold'>(B) </span>15\qquad<span class='latex-bold'>(C) </span>20\qquad<span class='latex-bold'>(D) </span>25\qquad<span class='latex-bold'>(E) </span>\text{30}
VietaalgebrapolynomialsymmetryRational Root Theoremsystem of equationsAMC
Sequences of Multiples

Source: 2015 amc 10b #16

2/26/2015
Al, Bill, and Cal will each randomly be assigned a whole number from 11 to 1010, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's? <spanclass=′latex−bold′>(A)</span>91000<spanclass=′latex−bold′>(B)</span>190<spanclass=′latex−bold′>(C)</span>180<spanclass=′latex−bold′>(D)</span>172<spanclass=′latex−bold′>(E)</span>2121<span class='latex-bold'>(A) </span> \dfrac{9}{1000} \qquad<span class='latex-bold'>(B) </span> \dfrac{1}{90} \qquad<span class='latex-bold'>(C) </span> \dfrac{1}{80} \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{72} \qquad<span class='latex-bold'>(E) </span> \dfrac{2}{121}
probabilityAMC