X is even, which MUST BE odd??

[gmatpup]

I don't understand why my answer was wrong.. please help!!!!

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

A. 3x/2

B. 3x/2 + 1

C. 3x^2

D. 3x^2/2

E. 3x^2/2 + 1



I chose B.. I plugged in numbers and it seemed to be right but clearly I was wrong.. It said the answer is E


any explanation would be super helpful!! thanks

[gmatscottsdale]

B is wrong because if you plug in x = 1, you get:

3*2/2 + 1 = 3*1 + 1 = 4 which is even.

3*even/2 might still give you odd because there is a 2 in the denominator.

If you look at E, you have 3*(even)^2/2 => ALWAYS EVEN because EVEN^2/2 always gives you even and anything multiplied with an even is even (In this case, 3*even).

Hence, EVEN + 1 - gives you odd.

If you want to avoid all this complexity, let's plug in 2 for x, we get 3*4/2 + 1 = 3*2 + 1 - 7

Credited Response: E

[neelgandham]

I don't understand why my answer was wrong.. please help!!!!

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

A. 3x/2; - If x=2, the expression 3x/2 is odd. If x=4, the expression 3x/2 is even

B. 3x/2 + 1 - If x=2, the expression 3x/2 + 1 is even. If x=4, the expression 3x/2 + 1 is odd

C. 3x^2 - 3*even*even = Even number

D. 3x^2/2 - 3*even*even/2 = Even number

E. 3x^2/2 + 1 - Need not check , It is your answer

In Red !

p.s: Can you please post any Data Sufficient questions here => https://www.beatthegmat.com/data-sufficiency-f7.html

[Anurag@Gurome]

I don't understand why my answer was wrong.. please help!!!!

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

A. 3x/2

B. 3x/2 + 1

C. 3x^2

D. 3x^2/2

E. 3x^2/2 + 1



I chose B.. I plugged in numbers and it seemed to be right but clearly I was wrong.. It said the answer is E


any explanation would be super helpful!! thanks

Plugging in numbers is definitely the best way for problems like this one. Neelgandham has explained it well.