Hashtag Operation
Pro Problems > Math > Number and Quantity > Number Theory > Star OperationsHashtag Operation
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Commutative Operation
The operation * is defined as follows: x * y = (ax + b)(by + a), for some real numbers a and b. Under what conditions is this operation commutative?
Star and Pound Operations
If a * b = (a + b)2, and a # b = (a - b)2, find x such that (2 * x) # (x * 1) = 81
Star Operation with Cubes
Non-Commutative Operation
x ♦ 2x = 2x ♦ x.
Note that this operation is not commutative; the order of operands cannot be exchanged without altering the result of the operation.
h and k
x * y = x2 - y2 + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).
Diamond Operation
If the operation ♦ is defined as follows: a ♦ b = a2 - b2 , and 
18 ♦ (x ♦ 8) = 6 ♦ 1, find all possible values of x.
Guess the Star
There exists a star (*) operation for which the following equations are true:
2 * 3 = 10
5 * 2 = 35
3 * 6 = 27
8 * 7 = 120
Find a star operation rule which satisfies all of these equations, and then use your rule to calculate the following:
10 * 11 = ?
Triangular Operation
The arrangementFractional Operation
Blogs on This Site
Like us on Facebook to get updates about new resources