Grades 1-2 Video Solutions 2020-2020Levels12prob22

Video Transcription

Problem number 22, Rue wrote each of the numbers 1, 2, 3, 4, and 5 in one of the circles in such a way that the sum of the numbers in the row is equal to the sum of the numbers  in the column. What number can be written in the circle of the question mark? A, only 5, B, 2, 3, or 4, C, only 3, D, only 1 or 3, E, 1, 3, or 5.  When we add the sums, the number in the middle will be included in both sums. So we need to find what number we can put here and then make two pairs of equal sums  out of the other four numbers. Another thing to note is that we have two even numbers and three odd numbers.  If we put one of the even numbers in the middle, we will be left with three odd numbers and one even number, so one of our sums will be even and one odd, so that will not work.  So we already know that 2 or 4 cannot go in the middle.  Let's look at the three choices of 1, 3, and 5. If we put 1 in the middle, the other numbers are 2, 3, 4, and 5.  We can make two equal sums by adding 3 and 4, which makes 7, and 2 and 5, which makes 7. So we can put 1 in the middle. For 3, we are left with numbers 1, 2, 4, and 5.  We can add 2 and 4 to make 6 and 1 and 5 to make 6, so 3 also works. If we put 5 in the middle, we have 1, 2, 3, and 4.  We add 2 and 3 to make 5 and 1 and 4 to make 5, so 5 also works as the number we can put in the middle.  So Rourou can put any of the numbers 1, 3, or 5 in the middle circle of the question mark. The answer is E.

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