If x is an even integer, which of the following must always be odd?

a. 3x/2
b. (3x/2)+1
c. 3x^2
d. (3x^2)/2
e. (3x^2)/2 + 1

Why is the answer d and not b???

Answer should be e

Just put any even integer as x and see which gives you an odd number - the question uses 'must'

First try 2-eliminate as many as possible (b,c,d) then try 4(a) - so you are left with e

yep, number plugging is definitely the method with the least hassle for problems like this one.

if you like theory, you can designate an arbitrary even integer as "2k" where k is any integer.
in that case, choice b = (6k/2) + 1 = 3k + 1, which is odd if k is even, but is even if k is odd.

still, it's much easier to plug in numbers; you won't have to go far (no farther than 4) before you're left with a unique answer. that will take way less time than grinding "2k" through all the answer choices AND working out the parity (even/odd) of the resulting expressions.