Question

Dashed arrows mean addition,
solid arrows mean
multiplication, and the circles
must be filled with integers.
Which number could go in the
place of the question mark?​

Answer 1

Given :

• Product of top three circles = 32
• Product of bottom two circles = 60

To find :

• Number in the circle marked ( ? )

Solution :

• As we can see from the question, 32 is the product of three numbers.
• Also, 60 is the product of two numbers.
• Hence, we write factors of 32 and 60.

• 32 = 1 × 2 × 16

             = 1 × 4 × 8

             = 2 × 4 × 4

             = 2 × 2 × 8

• 60 = 1 × 60

             = 2 × 30

             = 3 × 10

             = 4 × 15

             = 5 × 12

             = 6 × 10

• Also, the sum of two factors of 32 give the first factor of 60 and that of the next two factors give the second factor of 60.
• So from the given factors, we have to chose the numbers which satisfy our conditions.
• We can see that, 1 × 4 × 8 = 32
• 1 + 4 = 5 and 4 + 8 = 12
• 5 × 12 = 60
• In this way, we get our answer as 4.

Answer :

• The number that could go in the place of the question mark is 4.