MathDB

12

Part of 2012 AMC 10

Problems(2)

What Day of the Week?

Source: 2012 AMC10A Problem #12 and AMC12A #9

2/8/2012
A year is a leap year if and only if the year number is divisible by 400400 (such as 20002000) or is divisible by 44 but not by 100100 (such as 20122012). The 200th200\text{th} anniversary of the birth of novelist Charles Dickens was celebrated on February 77, 20122012, a Tuesday. On what day of the week was Dickens born?
<spanclass=′latex−bold′>(A)</span> Friday<spanclass=′latex−bold′>(B)</span> Saturday<spanclass=′latex−bold′>(C)</span> Sunday<spanclass=′latex−bold′>(D)</span> Monday<spanclass=′latex−bold′>(E)</span> Tuesday <span class='latex-bold'>(A)</span>\ \text{Friday} \qquad<span class='latex-bold'>(B)</span>\ \text{Saturday} \qquad<span class='latex-bold'>(C)</span>\ \text{Sunday} \qquad<span class='latex-bold'>(D)</span>\ \text{Monday} \qquad<span class='latex-bold'>(E)</span>\ \text{Tuesday}
summer programMathPathFTWmodular arithmeticalgorithmAMC
Finding Distance Between Points

Source: 2012 AMC10B Problem #12

2/23/2012
Point BB is due east of point AA. Point CC is due north of point BB. The distance between points AA and CC is 10210\sqrt{2} meters, and ∠BAC=45∘\angle BAC=45^{\circ}. Point DD is 2020 meters due north of point CC. The distance ADAD is between which two integers?
<spanclass=′latex−bold′>(A)</span> 30 and 31<spanclass=′latex−bold′>(B)</span> 31 and 32<spanclass=′latex−bold′>(C)</span> 32 and 33<spanclass=′latex−bold′>(D)</span> 33 and 34<spanclass=′latex−bold′>(E)</span> 34 and 35 <span class='latex-bold'>(A)</span>\ 30\text{ and }31\qquad<span class='latex-bold'>(B)</span>\ 31\text{ and }32\qquad<span class='latex-bold'>(C)</span>\ 32\text{ and }33\qquad<span class='latex-bold'>(D)</span>\ 33\text{ and }34\qquad<span class='latex-bold'>(E)</span>\ 34\text{ and }35
Pythagorean TheoremgeometryAMC