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

BTGmoderatorLU wrote:Source: GMAT Prep

If x is even integer, which of the following must be an odd integer?
$$A.\ \frac{3x}{2}$$
$$B.\ \frac{3x}{2}+1$$
$$C.\ 3x^2$$
$$D.\ \frac{3x^2}{2}$$
$$E.\ \frac{3x^2}{2}+1$$
The OA is E.

A quick approach is the plug in a even number for x and see what happens.
A super easy number to use us x = 0

We get.....
A) (3)(0)/2 = 0, which is NOT odd. ELIMINATE A.
B) (3)(0)/2 + 1 = 1, which IS odd. KEEP B.
C) (3)(0)² = 0, which is NOT odd. ELIMINATE C.
D) (3)(0²)/2 = 0, which is NOT odd. ELIMINATE D.
E) (3)(0²)/2 + 1 = 1, which IS odd. KEEP E.

We're down to just B and E
Now plug in a different value for x.
How about x = 2
We get.....
B) (3)(2)/2 + 1 = 4, which is NOT odd. ELIMINATE B.

Answer: E

ASIDE:
E) (3)(2²)/2 + 1 = 7, which IS odd. KEEP E.

Cheers,
Brent

BTGmoderatorLU wrote:Source: GMAT Prep

If x is even integer, which of the following must be an odd integer?
$$A.\ \frac{3x}{2}$$
$$B.\ \frac{3x}{2}+1$$
$$C.\ 3x^2$$
$$D.\ \frac{3x^2}{2}$$
$$E.\ \frac{3x^2}{2}+1$$

Since x is even (i.e., it has at least one factor of 2), 3x^2 must have at least two factors of 2. So 3x^2/2 would still be even and 3x^2/2 + 1 would then be odd since even + 1 = odd.

Answer: E