MathDB

2

Part of 2002 AMC 10

Problems(3)

Symmetric Quotient Function

Source:

2/11/2008
For the nonzero numbers a a, b b, c c, define (a,b,c)\equal{}\frac{a}{b}\plus{}\frac{b}{c}\plus{}\frac{c}{a}. Find (2,12,9) (2,12,9).
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 4 \qquad <span class='latex-bold'>(B)</span>\ 5 \qquad <span class='latex-bold'>(C)</span>\ 6 \qquad <span class='latex-bold'>(D)</span>\ 7 \qquad <span class='latex-bold'>(E)</span>\ 8
function
Function on Three Variables

Source:

2/26/2008
For the nonzero numbers a a, b b, and c c, define (a,b,c)\equal{}\frac{abc}{a\plus{}b\plus{}c}. Find (2,4,6)(2,4,6).
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 24 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ 4 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 24
Sum of Eleven Consecutive Integers

Source:

4/2/2013
The sum of eleven consecutive integers is 20022002. What is the smallest of these integers?
<spanclass=′latex−bold′>(A)</span>175<spanclass=′latex−bold′>(B)</span>177<spanclass=′latex−bold′>(C)</span>179<spanclass=′latex−bold′>(D)</span>180<spanclass=′latex−bold′>(E)</span>181<span class='latex-bold'>(A) </span>175\qquad<span class='latex-bold'>(B) </span>177\qquad<span class='latex-bold'>(C) </span>179\qquad<span class='latex-bold'>(D) </span>180\qquad<span class='latex-bold'>(E) </span>181
MATHCOUNTSanalytic geometry