MathDB

6

Part of 2004 AMC 10

Problems(2)

Problem: 2004 AMC 10 #6

Source:

2/1/2007
Bertha has 6 6 daughters and no sons. Some of her daughters have 6 6 daughters and the rest have none. Bertha has a total of 30 30 daughters and granddaughters, and no great-grand daughters. How many of Bertha's daughters and granddaughters have no daughters? <spanclass=′latex−bold′>(A)</span> 22<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 24<spanclass=′latex−bold′>(D)</span> 25<spanclass=′latex−bold′>(E)</span> 26 <span class='latex-bold'>(A)</span>\ 22\qquad <span class='latex-bold'>(B)</span>\ 23\qquad <span class='latex-bold'>(C)</span>\ 24\qquad <span class='latex-bold'>(D)</span>\ 25\qquad <span class='latex-bold'>(E)</span>\ 26
Perfect Squares

Source:

1/15/2009
Which of the following numbers is a perfect square? <spanclass=′latex−bold′>(A)</span> 98!⋅99!<spanclass=′latex−bold′>(B)</span> 98!⋅100!<spanclass=′latex−bold′>(C)</span> 99!⋅100!<spanclass=′latex−bold′>(D)</span> 99!⋅101!<spanclass=′latex−bold′>(E)</span> 100!⋅101! <span class='latex-bold'>(A)</span>\ 98!\cdot 99!\qquad <span class='latex-bold'>(B)</span>\ 98!\cdot 100!\qquad <span class='latex-bold'>(C)</span>\ 99!\cdot 100!\qquad <span class='latex-bold'>(D)</span>\ 99!\cdot 101!\qquad <span class='latex-bold'>(E)</span>\ 100!\cdot 101!