Track / Stage 4 / 270 of 340 #530 of 2000

Problem 530

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

5. Real numbers $x, y$ satisfy $[x] \cdot[y]=2$ , then $[x+1] \cdot[y-1]$ has $\qquad$ possible values.
(Where $[x]$ represents the greatest integer not greater than $x$ , for example: $[3.7]=3,[-3.2]=-4,[0]=0$ )

Your answer

Official solution

$2$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.