Let \(S\) be the sum of the base 10 logarithms of all the proper divisors of 1000000. What is the integer nearest to \(S\)?
Tags: logarithms,divisors,factors
Source: AIME 1986 I Q8
Elo Rating: 1500.00
Quadrilateral \(ABCD\) is a trapezoid, \(AD = 15\), \(AB = 50\), \(BC = 20\), and the altitude is \(12\). What is the area of the trapezoid? [asy] pair A,B,C,D; A=(3,20); B=(35,20); C=(47,0); D=(0,0); draw(A--B--C--D--cycle); dot((0,0)); dot((3,20)); dot((35,20)); dot((47,0)); label("A",A,N); label("B",B,N); label("C",C,S); label("D",D,S); draw((19,20)--(19,0)); dot((19,20)); dot((19,0)); draw((19,3)--(22,3)--(22,0)); label("12",(21,10),E); label("50",(19,22),N); label("15",(1,10),W); label("20",(41,12),E);[/asy] $$ \textbf{(A)}600\qquad\textbf{(B)}650\qquad\textbf{(C)}700\qquad\textbf{(D)}750\qquad\textbf{(E)}800 $$
Tags: geometry,area,pythagoras
Source: AMC 8 2011 A Q20
Elo Rating: 1500.00