MathDB

11

Part of 2022 AMC 10

Problems(2)

Ted's Mistake

Source: 2022 AMC 10A #11

11/11/2022
Ted mistakenly wrote 2m⋅140962^m \cdot \sqrt{\frac{1}{4096}} as 2⋅14096m2\cdot \sqrt[m]{\frac{1}{4096}}. What is the sum of all real numbers mm for which these two expressions have the same value?
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>9<span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>9
AMCAMC 102022 AMC2022 AMC 10aalgebra
AMC logic

Source: AMC 10b Problem 11

11/17/2022
All the high schools in a large school district are involved in a fundraiser selling T-shirts. Which of the choices below is logically equivalent to the statement “No school bigger than Euclid HS sold more T-shirts than Euclid HS”?
(<spanclass=′latex−bold′>A</span>)(<span class='latex-bold'>A</span>) All schools smaller than Euclid HS sold fewer T-shirts than Euclid HS. (<spanclass=′latex−bold′>B</span>)(<span class='latex-bold'>B</span>) No school that sold more T-shirts than Euclid HS is bigger than Euclid HS. (<spanclass=′latex−bold′>C</span>)(<span class='latex-bold'>C</span>) All schools bigger than Euclid HS sold fewer T-shirts than Euclid HS. (<spanclass=′latex−bold′>D</span>)(<span class='latex-bold'>D</span>) All schools that sold fewer T-shirts than Euclid HS are smaller than Euclid HS. (<spanclass=′latex−bold′>E</span>)(<span class='latex-bold'>E</span>) All schools smaller than Euclid HS sold more T-shirts than Euclid HS.
AMCAMC 10AMC 10 B