GMAT Math - Defined Functions Review
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Verbal
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Defined Functions
Defined functions are common on the GMAT, and most students struggle with them. Yet once you get used to them, defined functions can be some of the easiest problems on the test. In this type of problem, you will be given a symbol and a property that defines the symbol.
Example:
Define x # y by the equation x # y = xy - y. Then 2 # 3 =
(A) 1
(B) 3
(C) 12
(D) 15
(E) 18
From the above definition, we know that x # y = xy - y. So all we have to do is replace x with 2 and y with 3 in the definition: 2 # 3 = 2(3) - 3 = 3. Hence, the answer is (B).
Example:
Define the symbol * by the following equation: x* = 2 - x, for all non-negative x. If (2 - x)* = (x - 2)*, then x =
(A) 0
(B) 1
(C) 2
(D) 4
(E) 6
(2 - x)* = (x - 2)*
2 - (2 - x) = 2 - (x - 2)
2 - 2 + x = 2 - x + 2
x = 4 - x
2x = 4
x = 2
The answer is (C).
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