MathDB

6

Part of 2016 AMC 10

Problems(2)

Sums of integers

Source: Problem #6 2016 AMC 10A

2/3/2016
Ximena lists the whole numbers 11 through 3030 once. Emilio copies Ximena's numbers, replacing each occurrence of the digit 22 by the digit 11. Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 26<spanclass=′latex−bold′>(C)</span> 102<spanclass=′latex−bold′>(D)</span> 103<spanclass=′latex−bold′>(E)</span> 110<span class='latex-bold'>(A)</span>\ 13\qquad<span class='latex-bold'>(B)</span>\ 26\qquad<span class='latex-bold'>(C)</span>\ 102\qquad<span class='latex-bold'>(D)</span>\ 103\qquad<span class='latex-bold'>(E)</span>\ 110
2016 AMC 10AAMCAMC 10AMC 10 A
Laura and her adding

Source: Problem #6 2016 AMC 10B

2/21/2016
Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number SS. What is the smallest possible value for the sum of the digits of SS?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> 21<span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 4\qquad<span class='latex-bold'>(C)</span>\ 5\qquad<span class='latex-bold'>(D)</span>\ 15\qquad<span class='latex-bold'>(E)</span>\ 21
AMCAMC 102016 AMC 10BAMC 10 B