A logic problem by Nashita Rahman

Logic Level pending

Three-digit number A A A ‾ \overline{AAA} , where A A is a positive integer from 1 to 9, is divisible by a two-digit number X Y ‾ \overline{XY} and 3 × A × X Y ‾ = A A A ‾ 3 \times A \times \overline{XY} = \overline{AAA} .

Find the number X Y ‾ \overline{XY} ?


The answer is 37.

Nashita Rahman by Nashita Rahman , 21, India

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2 solutions

Chew-Seong Cheong
Aug 25, 2016

3 × A × X Y ‾ = A A A ‾ ⟹ X Y ‾ = A A A ‾ 3 A = 111 3 = 37 \begin{aligned} 3 \times A \times \overline{XY} & = \overline{AAA} \\ \implies \overline{XY} & = \frac {\overline{AAA}}{3A} \\ & = \frac {111}3 \\ & = \boxed{37} \end{aligned}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Nashita Rahman
Aug 24, 2016

Take any 3-digit number AAA .

AAA can be 111,222,......., 999

It is given that AAA is divisible by 3A.

111÷3=37

222÷6=37.......

Hence , XY=37

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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