MathDB

16

Part of 2014 AMC 12/AHSME

Problems(2)

Sum of Digits Equals 1000

Source: 2014 AMC 12A #16/10A #20

2/5/2014
The product (8)(888…8)(8)(888\ldots 8), where the second factor has kk digits, is an integer whose digits have a sum of 10001000. What is kk?
<spanclass=′latex−bold′>(A)</span>901<spanclass=′latex−bold′>(B)</span>911<spanclass=′latex−bold′>(C)</span>919<spanclass=′latex−bold′>(D)</span>991<spanclass=′latex−bold′>(E)</span>999<span class='latex-bold'>(A) </span>901\qquad <span class='latex-bold'>(B) </span>911\qquad <span class='latex-bold'>(C) </span>919\qquad <span class='latex-bold'>(D) </span>991\qquad <span class='latex-bold'>(E) </span>999\qquad
AMC
Cubic polynomial coefficients

Source: AMC 12B #16

2/20/2014
Let PP be a cubic polynomial with P(0)=k,P(1)=2k,P(0) = k, P(1) = 2k, and P(−1)=3kP(-1) = 3k. What is P(2)+P(−2)P(2) + P(-2)?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>k<spanclass=′latex−bold′>(C)</span>6k<spanclass=′latex−bold′>(D)</span>7k<spanclass=′latex−bold′>(E)</span>14k <span class='latex-bold'>(A) </span>0 \qquad<span class='latex-bold'>(B) </span>k \qquad<span class='latex-bold'>(C) </span>6k \qquad<span class='latex-bold'>(D) </span>7k\qquad<span class='latex-bold'>(E) </span>14k\qquad
algebrapolynomialsystem of equationsAMC