MathDB
Logical guessing game!

Source: 2021 Fall AMC10B P10

November 17, 2021
AMCAMC 10AMC 10 B

Problem Statement

Fourty slips of paper numbered 11 to 4040 are placed in a hat. Alice and Bob each draw one number from the hat without replacement, keeping their numbers hidden from each other. Alice says, "I can't tell who has the larger number." Then Bob says, "I know who has the larger number." Alice says, "You do? Is your number prime?" Bob replies, "Yes." Alice says, "In that case, if I multiply your number by 100100 and add my number, the result is a perfect square. " What is the sum of the two numbers drawn from the hat?
<spanclass=′latex−bold′>(A)</span>27<spanclass=′latex−bold′>(B)</span>37<spanclass=′latex−bold′>(C)</span>47<spanclass=′latex−bold′>(D)</span>57<spanclass=′latex−bold′>(E)</span>67<span class='latex-bold'>(A) </span>27\qquad<span class='latex-bold'>(B) </span>37\qquad<span class='latex-bold'>(C) </span>47\qquad<span class='latex-bold'>(D) </span>57\qquad<span class='latex-bold'>(E) </span>67
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