Grades 1-2 Video Solutions 2019-2019Levels12prob23

Video Transcription

Problem number 23. Peter chose a square of four cells in the table, so the sum of the four numbers inside the square is greater than 63.  Which of the following numbers must be in the chosen square? A, 14. B, 15. C, 17. D, 18. E, 20.  When the problem asks about a four-cell square within the table, it's asking about a square like this.  And the sum is the four numbers inside such a square.  The problem asks us to find the squares where the sum is greater than 63. In order for a sum to be that big, the numbers have to be fairly large.  For example, if we chose the first square with 1, 2, 6, and 7, the sum would only be 16. So we're going to start from the highest numbers in the table.  Let's look at this square first.  The numbers are 14, 15, 19, and 20. 4 plus 5 is 9, plus 9 gives us 18. Carry the 1, 2 plus 1 is 3, 4, 5, 6. This square will have a sum of 68. So this would be a square that works.  We need to find the other squares so that we can figure out which of the numbers listed has to be in all of those squares.  The next smallest sum of numbers would be taking this square.  The numbers are 13, 14, 18, and 19.  4 plus 8 is 12. 3 plus 9 is also 12. 12 plus 12 is 24. Carry the 2. It's 2, 3, 4, 5, 6. That's 64. So this square also works. Let's try the next smaller square this direction.  The numbers here are 12, 13, 17, and 18. 2 plus 8 is 10. 7 and 3 is 10. 20. This time it's only 60, so that square is not one that we can use.  If we try the square of 11, 12, 16, and 17, the sum would be even smaller, so that's not going to work. If we try going up on the table, for example, taking these numbers.  9, 10, 14, and 15. 4 plus 5 is 9, plus 9 gives us 18. Carry a 1.  This also is not going to work. We have two squares that work. This one with 14, 15, 19, and 20. And this one with 13, 14, 18, and 19.  There are two numbers that are common to both squares. They are 14 and 19. However, of these, only 14 is listed as one of our choices. 19 is not one of the choices listed.  The problem asks which of the numbers below must be in the chosen square. And a number 14 is the only number that has to be in the square, regardless of which square is chosen.  So the answer is A, 14.

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