MathDB

10

Part of 2015 AMC 10

Problems(2)

abcd Rearrangements

Source: 2015 10A #10

2/4/2015
How many rearrangements of abcdabcd are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either abab or baba.
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>4 <span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>4
geometrygeometric transformationreflectionsymmetryAMC
Product of Negative Numbers

Source: 2015 amc 10b #10

2/26/2015
What are the sign and units digit of the product of all the odd negative integers strictly greater than −2015-2015? <spanclass=′latex−bold′>(A)</span>It is a negative number ending with a 1.<span class='latex-bold'>(A) </span> \text{It is a negative number ending with a 1.} <spanclass=′latex−bold′>(B)</span>It is a positive number ending with a 1.<span class='latex-bold'>(B) </span> \text{It is a positive number ending with a 1.} <spanclass=′latex−bold′>(C)</span>It is a negative number ending with a 5.<span class='latex-bold'>(C) </span> \text{It is a negative number ending with a 5.} <spanclass=′latex−bold′>(D)</span>It is a positive number ending with a 5.<span class='latex-bold'>(D) </span> \text{It is a positive number ending with a 5.} <spanclass=′latex−bold′>(E)</span>It is a negative number ending with a 0.<span class='latex-bold'>(E) </span> \text{It is a negative number ending with a 0.}
AMC