You are given a mathematical question described with a circumscribed mathematical vocabulary. Questions in this task usually contain some variables (e.g. X, Y), equations (e.g. X+Y=3) and some relationships (X is greater than Y). Often you need to find the value of the variable using equations and relationships. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge. Give only one answer for each question.

Sequence Y: 5, 10, 15, ... Sequence Z: 3, 6, 12, ... The first term in Sequence Y is 5, and each term after the first is 5 more than the preceding term. The first term in sequence Z is 3, and each term after the first is 2 times the preceding term. What is the least value of x such that the xth term of Sequence Z is more than three times the xth term of Sequence Y?
(A)5 (B)6 (C)7 (D)8 (E)9
B
Sequence Y: 5, 10, 15, ... Sequence Z: 3, 6, 12, ... The first term in sequence Y is 5 and the second term is 10. The third term is 15=10+5. In general each term after the first is five more than the preceding term. The first term in sequence Z is 3 and the second term is 6=3*2. The thirdtermis12=6*2.Ingeneraleachtermafterthefirstistimethesucceedingterm. \n\nWe want to find values of x>1 such that 3(5x)<2^x(3). This equality holds for x = 2 (when both sides are 30), but it fails for x = 1 (when both sides are 30). We see that increasing x by 1 will decrease both sides of our inequality by a factor of 2 or more; therefore we only need to check odd values of X greater than one to see if they work. Let's check X = 3: \n\n30 < 6(27) \/ True since 54 > 30 So we have found a value of x where our inequality holds true! Since this value was odd we know it will hold true for all higher positive integer values as well; therefore there isn't any need to check further so our answer should be B)..