MathDB
To a Friend's House We Go!

Source: 2017 AMC 8 #8

November 22, 2017
AMC 8

Problem Statement

Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true." (1) It is prime. (2) It is even. (3) It is divisible by 7. (4) One of its digits is 9. This information allows Malcolm to determine Isabella's house number. What is its units digit?
<spanclass=latexbold>(A)</span>4<spanclass=latexbold>(B)</span>6<spanclass=latexbold>(C)</span>7<spanclass=latexbold>(D)</span>8<spanclass=latexbold>(E)</span>9<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>9