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Number Theory (No U)

Source: 2018 AMC 8 #7

November 20, 2018
AMC 8number theory2018 AMC 8

Problem Statement

The 55-digit number 2‾\underline{2} 0‾\underline{0} 1‾\underline{1} 8‾\underline{8} U‾\underline{U} is divisible by 99. What is the remainder when this number is divided by 88?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>7<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>5\qquad<span class='latex-bold'>(D) </span>6\qquad<span class='latex-bold'>(E) </span>7
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