If t is and odd integer, which of the following must be an even integer?
Let's analyze each of the given expressions:
t - 2: If t is an odd integer, subtracting 2 from it will result in an odd integer minus an even integer, which will always be an odd integer.
2t + 3: If t is an odd integer, multiplying it by 2 will result in an even integer. Adding 3 to an even integer will still result in an odd integer.
4t + 1: If t is an odd integer, multiplying it by 4 will result in an even integer. Adding 1 to an even integer will result in an odd integer.
3t + 1: If t is an odd integer, multiplying it by 3 will result in an odd integer. Adding 1 to an odd integer will result in an even integer.
So, among the given options, 3t + 1 must be an even integer when t is an odd integer.
Short Tricks:
Option Check =>
least odd integer is: 1
Now, 1-2 = -1
2*1+3 = 5
4*1+1 = 5
3*1+1 = 4 (Even)
N.B: you may also check option using interger = 3, 5, 7…
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