Question

Replace y by a suitable digit so that 61y6 is divisible by 3

Answer 1

$\Huge{\boxed{Answer:}}$



$\boxed{ test \: of \: divisiblity \: of \: 3: }$


$according \: \: to \: \: this \: \: any \: \: number \\ is \: \: divisible \: \: by \: \: 3 \: \: if \: \: the \: \: sum \\ of \: \: its \: \: digits \: \: is \: \: divisible \: \: by \: \: 3.$



$sum \: \: of \: \: the \: \: digits \: \: in \: \: 61y6: \\ \\ 6 + 1 + y + 6 = 13 + y. \\ \\ 13 + y \: \: should \: \: leave \: \: a \\ remainder \: \: of \: \: 0 \: \: when \: \: divided \\ by \: \: 3.$



$the \: \: smallest \: \: number \: \: that \\ satisfies \: \: this \: is \: \: 2. \\ \\ therefore \: \: y = 2.$


$y \: \: can \: \: also \: \: be \: \: 5 \: \: or \: \: 8. \\ \\ note: we \: \: can \: \: see \: \: that \: \: though \\ 12 \: \: is \: \: closer \: \: to \: \: 13 \: \: we \: \: dont \\ \: take \: \: this \: \: as \: \: a \: \: value \: \: for \: \: y \: \: as \\ it \: \: is \: \: only \: \: the \: numbers \: \: after \\ 13 \: \: that \: \: should \: \: be \: taken \: \: into \\ consideration \: \: for \: \: the \: \: value \\ of \: \: y.$