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f is a function mapping from {1, 2, 3} to {1, 2, 3, 4, 5}. x + f(x) is odd. How many possible c

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by Max@Math Revolution » Wed Jul 22, 2020 7:25 am

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[GMAT math practice question]

f is a function mapping from {1, 2, 3} to {1, 2, 3, 4, 5}. x + f(x) is odd. How many possible cases of f(x) do we have?

A. 9
B. 10
C. 11
D. 12
E. 13
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Re: f is a function mapping from {1, 2, 3} to {1, 2, 3, 4, 5}. x + f(x) is odd. How many possible c

by Max@Math Revolution » Fri Jul 24, 2020 12:33 am
=>

If x is an odd number, then f(x) is an even number.
If x is an even number, then f(x) is an odd number.
Then the possible values of f(1) and f(3) are 2 and 4. The number of possible cases for f(1) and f(3) is 2.
The possible values of f(2) are 1, 3, and 5. The number of possible cases for f(2) = 3.

Thus. the number of possible cases for the function f(x) is 2·2·3 = 12.

Therefore, D is the correct answer.
Answer: D
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