Grades 3-4 Video Solutions 2025-2025_3-4

Video Transcription

Question 15. Maria fills the circles with the numbers 1, 2, 3, 4, 5, 6, and 7. The number in each of the lower circles is equal to the sum of the two numbers in the  connected circles above it. What number goes in the circle with a star? Let's draw the diagram and start off with what we know. We can see that one of the circles  already has a 6 filled in. Since the numbers are between 1 and 7, the only way for the bottom circle here to be valid given the rules is 7, since there is no other set of numbers  that will give us a sum. It has to be bigger than 6. And we do 6 plus 1 to get 7, so the 1 will have to be here. Next, let's take a look at the rightmost bottom  circle. We know that this will have to be the sum of the two other unknown circles above it, and we are left with 2, 3, 4, and 5. The only number that could fit in here,  since the 1 is already taken and won't be part of this equation, is 5. To get 5, we do 2 and 3. And, when we look at the 1 and the 3 above the star, we know that those will  sum up to 4, which is the only number left to fill in, so the answer will be C, 4.

Video Summary

Maria arranges numbers 1 through 7 in circles such that each lower circle contains the sum of the two numbers in the connected upper circles. One circle already contains the number 6. To complete the structure, Maria deduces that the numbers 6 and 1 must pair to form the number 7 in a lower circle, while 2 and 3 must sum to 5 in another. Given that two of the numbers above the starred circle are 1 and 3, the sum, and thus the number in the starred circle, is 4. Therefore, the number in the starred circle is 4.

Keywords

number arrangement

circle puzzle

sum structure

number pairing

logic deduction