MathDB

7

Part of 2022 MIG

Problems(2)

2022 A Individual #7

Source:

4/28/2022
Consider the rectangular strip of length 1212 below, divided into three rectangles. The distance between the centers of two of the rectangles is 44. What is the length of the other rectangle?
[asy] size(120); draw((0,0)--(12,0)--(12,1)--(0,1)--cycle); draw((8,1)--(8,0)); draw((3,1)--(3,0)); dot((1.5,0.5)); dot((5.5,0.5)); draw((1.5,0.5)--(5.5,0.5)); [/asy]
<spanclass=latexbold>(A)</span>2.5<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>3.5<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>4.5<span class='latex-bold'>(A) </span>2.5\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>3.5\qquad<span class='latex-bold'>(D) </span>4\qquad<span class='latex-bold'>(E) </span>4.5
geometry2022 A Individual
2022 B Individual #7

Source:

4/30/2022
Alice, Bob, and Charlie are each thinking of a number. Alice's number differs from Bob's number by 22. Bob's number differs from Charlie's number by 66. Charlie's number differs from Alice's number by NN. What is the sum of all possible values for NN? <spanclass=latexbold>(A)</span>4<spanclass=latexbold>(B)</span>6<spanclass=latexbold>(C)</span>7<spanclass=latexbold>(D)</span>12<spanclass=latexbold>(E)</span>14<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>12\qquad<span class='latex-bold'>(E) </span>14
2022 B Individual