VERY UNUSUAL SYMBOLS

Sometimes there will be unusual symbols on the test that require you to perform strange operations. Actually, unusual symbols seem to pop up a lot in math, although the ones you may run into on the SAT or the ACT can be beyond strange or even silly. However, the trick is to carefully follow the directions. Usually, you just have to plug in.

Example: Let (abc)* = (b+c). Find (582)*.

Answer: 2500

Solution: (582)* = (8 +2) = (25)(10) = 2500

Example: Let n^ = . Find 5^ + 3^.

Answer:

Solution: This is a straight-forward plug in:

5^ + 3^ =

.

Example: Let n^ =. If b^ = 15, find b.

Caution: Here is a problem that looks like the last problem looking but that requires working backward! Note that the value of b^ has been given, and that we are asked to find b, not b^.

Answer: b =

Solution:

b^ = and b^ = 15. Therefore, = 15

8 = 15 ( b+3)

8 = 15b + 45

8 - 45 = 15b

- 37 = 15b

= b

Example: Let a#b = 3a - . Find 3#(4#5).

Answer: -160

Solution: Plug in. The parentheses suggest that (4#5) is done first.

3#(4#5) = 3#(3·4 - ) = 3#(12 - 25)

= 3#(-13)

= 3·3 -

= 9 - 169

= -160