Grades 3-4 Video Solutions 2023-2023_3-4

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Problem number 14. The metro line has six stations, A, B, C, D, E, and F. The train stops at every station. When it reaches one of the two end stations, it changes its direction.  The train engineer started driving at station B, and her first stop was station C. Which station will be her 96th stop?  Let's try to see if there's a pattern so we don't have to count all the way up to 96 to find the answer.  Here's a close-up of the picture. This is where the train is right now, and we're told that the first stop is C. So the train is going this direction, so the first stop.  I'll make D the second stop, E the third stop, F the fourth, and then the train starts going the other direction.  We're already at F, so the fifth stop will be E, D, C, B will be 8, A will be the ninth stop, and again it starts going the other way.  B is the tenth stop, and then C is 11, D is 12, E is 13, F is 14, changes directions, 15 at E, 16 at D, and we have 17, 18, 19, and B is 20. So we've marked the first 20 stops.  Looking at these numbers, we see that all the stop numbers that end with a given digit are in the same column. All the 1's are under C, so 1 and 11, and we will have 21 here.  The 2's are under D, 3's are under E, F has all the numbers ending in 4, then E again also has numbers ending in 5, and D has numbers ending in 6.  The number we're looking for ends in a 6, so it will end up being in the column of the D.  So the answer is D.

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