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

2023_3-4_11

Video Transcription

Problem number 11. Andrew has a 60 cm ruler. Unfortunately, some of the markings have faded.  He can still measure the lengths 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, and 60 cm using his ruler only once. Which is his ruler?  Looking at the answer choices, in each one, there are only a few of the markings shown. Andrew will have to use subtraction in order to find some of the lengths.  For example, if he had a ruler that only showed 20, and he knew that the whole ruler was 60 cm long, he could measure 60 cm using the whole ruler,  he could measure 20 cm up to the marking, and he could also measure 40 cm. 60 minus 20 is 40.  So we have to figure out which of these rulers allows us to make all six of these measurements. Looking at A, Andrew can measure 10 here,  he can measure 30 cm by going to the next marking, and he can measure 20 cm between the 10 and the 30. However, he can't measure 40 cm because this length is 30 cm.  He could measure 50 going from the other end to the 10, and all these rulers will be able to measure 60 cm because they're 60 cm long. So on A, he cannot measure 40 cm.  So this is not his ruler. In B, he can measure 60, he can measure 20, he can measure 40. From the other end, it's 20 cm to 40, and it's 40 cm to 20.  So on this one, the only lengths he can measure are the 20, 40, and 60, and he can't measure any of the ones that start with an odd digit. So this is not his ruler.  In ruler C, it's kind of the reverse of ruler A. He can measure 60, he can measure 50, 30,  he can measure 10 on this end, and he can measure 20 from 50 to 30. But again, he cannot measure 40. So that's not his ruler. Ruler D can measure 10 cm here, 20 cm.  From the other end, he can get 40 cm because 60 minus 20 is 40. He can also get 50 cm. He gets 60 for the whole length of the ruler, but there's no way to get 30 cm on this one.  So this is not his ruler. So E should be the answer. Let's check if we can get all the lengths. For the length of 10, we just need to measure to the marking of the 10.  For the length of 20, we measure from the end to 40 because 60 minus 40 is 20. For the length of 30 cm, we can go from the 10 to the 40. 40 minus 10 is 30.  For 40 cm, just go to the 40 mark. For 50 cm, we can go from the end to the 10 mark. 60 minus 10 is 50. And 60 cm is the whole length.  So E is the ruler that can make all those measurements. So this is Andrew's ruler.

Video Summary

In the problem, Andrew needs to determine which of his 60 cm rulers, marked at certain intervals, can still measure lengths of 10, 20, 30, 40, 50, and 60 cm despite faded markings. Each option involves using subtraction to calculate missing measurements. After evaluating each given ruler, only ruler E allows for all required measurements: 10 cm (straight to the 10 mark), 20 cm (60 - 40), 30 cm (40 - 10), 40 cm (straight to the 40 mark), 50 cm (60 - 10), and 60 cm (full length). Thus, ruler E is the correct choice for Andrew.