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P06 [Number Theory] - Turkish NMO 1st Round - 2002

Source:

August 7, 2014
modular arithmeticleast common multiple

Problem Statement

The thousands digit of a five-digit number which is divisible by 3737 and 173173 is 33. What is the hundreds digit of this number?
<spanclass=′latex−bold′>a)</span> 0<spanclass=′latex−bold′>b)</span> 2<spanclass=′latex−bold′>c)</span> 4<spanclass=′latex−bold′>d)</span> 6<spanclass=′latex−bold′>e)</span> 8 <span class='latex-bold'>a)</span>\ 0 \qquad<span class='latex-bold'>b)</span>\ 2 \qquad<span class='latex-bold'>c)</span>\ 4 \qquad<span class='latex-bold'>d)</span>\ 6 \qquad<span class='latex-bold'>e)</span>\ 8
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