MathDB

16

Part of 2002 AMC 10

Problems(3)

Symmetric System's Cyclic Sum

Source:

2/11/2008
If a\plus{}1\equal{}b\plus{}2\equal{}c\plus{}3\equal{}d\plus{}4\equal{}a\plus{}b\plus{}c\plus{}d\plus{}5, then a\plus{}b\plus{}c\plus{}d is \text{(A)}\ \minus{}5 \qquad \text{(B)}\ \minus{}10/3 \qquad \text{(C)}\ \minus{}7/3 \qquad \text{(D)}\ 5/3 \qquad \text{(E)}\ 5
Fraction Square

Source:

2/27/2008
For how many integers n n is \frac{n}{20\minus{}n} the square of an integer? <spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ 3 \qquad <span class='latex-bold'>(D)</span>\ 4 \qquad <span class='latex-bold'>(E)</span>\ 10
number theoryrelatively prime
A Fly in a Box

Source:

4/2/2013
Two walls and the ceiling of a room meet at right angles at point PP. A fly is in the air one meter from one wall, eight meters from the other wall, and 99 meters from point PP. How many meters is the fly from the ceiling?
<spanclass=′latex−bold′>(A)</span>13<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span>\sqrt{13}\qquad<span class='latex-bold'>(B) </span>\sqrt{14}\qquad<span class='latex-bold'>(C) </span>\sqrt{15}\qquad<span class='latex-bold'>(D) </span>4\qquad<span class='latex-bold'>(E) </span>\sqrt{17}
geometry3D geometryprism