The Official Online Forum of BdMO
https://matholympiad.org.bd/forum/
I know right. This is typically seen in BDMO selection and Divisional round.Asif Hossain wrote: ↑Sat Mar 27, 2021 10:01 pmWHY BDMO GIVES SUCH HAZYYYYYYYYYYYYYYY PROOOOOOOOOOBLEEEEEEEEEEEMMMMMMMMMMMMM
but it didn't said for every $x \in X$ for example if $7$ is inside $X$ but $3 \times 7=21$ isn't in $S$ but won't it be counted in $X$??Mehrab4226 wrote: ↑Sat Mar 27, 2021 9:45 pmYes, it said if $x$ is in $X$ and $3x$ in $S$. Then $3x$ must be in $X$. It implies that we cannot find any $x$ inside $X$ whose $3x$ if in $S$ not in $X$.Asif Hossain wrote: ↑Sat Mar 27, 2021 9:36 pmDidn't it said if "$x \in X$ and $3x \in S$" then $3x \in X$Mehrab4226 wrote: ↑Sat Mar 27, 2021 9:32 pm
Yes. The question said if $x$ is in $X$, then $3x$ is also in $X$. That is enough to let us know that $x$ can be any number in $X$
The question should have specified things a little more.Asif Hossain wrote: ↑Sun Mar 28, 2021 12:27 pmbut it didn't said for every $x \in X$ for example if $7$ is inside $X$ but $3 \times 7=21$ isn't in $S$ but won't it be counted in $X$??Mehrab4226 wrote: ↑Sat Mar 27, 2021 9:45 pmYes, it said if $x$ is in $X$ and $3x$ in $S$. Then $3x$ must be in $X$. It implies that we cannot find any $x$ inside $X$ whose $3x$ if in $S$ not in $X$.Asif Hossain wrote: ↑Sat Mar 27, 2021 9:36 pm
Didn't it said if "$x \in X$ and $3x \in S$" then $3x \in X$