Add++, 48 bytes

D,f,@,3@%2@%3*1+10*
D,g,@,0@-3>
_
$f,?
-G
$g,x
O

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This works on the theory that all McNugget numbers are greater than 3 after having gone through the following process:

• modulo the number by 3
• modulo the result by 2
• multiply that by 3
• add 1
• multiply the number by 10
• subtract that from the initial value
• negate the result

Which is what the function f does in the code above. The function g then checks whether it is less than 3 and returns a boolean value.

Add++, 35 bytes

D,f,@,A6$%0=@20$%0=A3$%0=A8<A43<s1<

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3 months later, I realised that this was invalid, and fixed it. Somehow, that golfed it by 13 bytes. This is a function that takes one argument and tests whether that argument is a Chicken McNugget number or not.

How it works

D,f,@, - Create a monadic (one argument) function called f (example argument: 3)
A - Push the argument again; STACK = [3 3]
 6 - Push 6; STACK = [3 3 6]
 $ - Swap the top two values; STACK = [3 6 3]
 % - Modulo; STACK = [3 3]
 0 - Push 0; STACK = [3 3 0]
 = - Are they equal? STACK = [3 0]
 @ - Reverse the stack; STACK = [0 3]
 20 - Push 20; STACK = [0 3 20]
 $ - Swap the top two values; STACK = [0 20 3]
 % - Modulo; STACK = [0 3]
 0 - Push 0; STACK = [0 3 0]
 = - Are they equal? STACK = [0 0]
 A - Push the argument; STACK = [0 0 3]
 3 - Push 3; STACK = [0 0 3 3]
 $ - Swap the top two values; STACK = [0 0 3 3]
 % - Modulo; STACK = [0 0 0]
 0 - Push 0; STACK = [0 0 0 0]
 = - Are they equal? STACK = [0 0 1]
 A - Push the argument; STACK = [0 0 1 3]
 8 - Push 8; STACK = [0 0 1 3 8]
 < - Less than; STACK = [0 0 1 0]
 A - Push the argument; STACK = [0 0 1 0 3]
 43 - Push 43; STACK = [0 0 1 0 3 43]
 < - Less than; STACK = [0 0 1 0 0]
 s - Sum; STACK = [1]
 1 - Push 1; STACK = [1 1]
 < - Less than; STACK = [0]