Grades 3-4 Video Solutions 2020-2020Levels34prob20

Video Transcription

Problem number 20. The teacher writes the numbers from one to eight on the board. The teacher then covers the numbers with triangles, squares, and circles.  If you add the four numbers covered by the triangles, the sum is 10. If you add the three numbers covered by the squares, the sum is 20. Which number is covered by the circle?  A, 3, B, 4, C, 5, D, 6, E, 7. In a problem like this, you usually don't need to figure out what every single shape represents.  It should be a fairly straightforward way to find the one number that you're looking for. We know that all the numbers on the board are the numbers 1, 2, 3, 4, 5, 6, 7, and 8.  We add all those together, we will get 1 plus 2 is 3, plus 3 is 6, plus 4 is 10, 5 plus 6 is 11, and 7 plus 8 is 15, which gives us 15 plus 11 is 26, plus 10 more, 36.  So the sum of all the numbers is 36. We also know the sum of all the numbers except for the circle, which is what we're looking for.  Because we know that all the triangles add up to 10, and all the squares add up to 20, which means that the sum of all the numbers other than the circle is 30.  So out of 36, the 7 numbers other than the circle are equal 30, so we are left with the number 6. That means that the circle covers up the number 6. Answer is D, 6.

Video Summary

The teacher covers numbers 1 to 8 with shapes, where triangles sum to 10 and squares to 20. To find the number under the circle, note that the total of numbers 1 to 8 is 36. The combined total for numbers under triangles and squares is 30. Subtracting 30 from 36 leaves 6, indicating the circle covers the number 6. Therefore, the answer is D, 6.