MathDB

16

Part of 2005 AMC 10

Problems(2)

Sum of the Digits of a Two-Digit Number

Source:

1/12/2009
The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is 6 6. How many two-digit numbers have this property? <spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 9<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 19 <span class='latex-bold'>(A)</span>\ 5\qquad <span class='latex-bold'>(B)</span>\ 7\qquad <span class='latex-bold'>(C)</span>\ 9\qquad <span class='latex-bold'>(D)</span>\ 10\qquad <span class='latex-bold'>(E)</span>\ 19
modular arithmetic
Roots of a quadratic

Source:

2/9/2006
The quadratic equation x2+mx+n=0x^2+mx+n=0 has roots that are twice those of x2+px+m=0x^2+px+m=0, and none of mm, nn, and pp is zero. What is the value of np\frac{n}{p}?
(A) 1(B) 2(C) 4(D) 8(E) 16\text{(A)} \ 1 \qquad \text{(B)} \ 2 \qquad \text{(C)} \ 4 \qquad \text{(D)} \ 8\qquad \text{(E)} \ 16
quadraticsalgebra