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

Question

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

Bunuel · Accepted Answer

One can spot right away that if x is any even number then x^2 is a multiple of 4, which makes \frac{x^2}{2} an even number and therefore \frac{3x^2}{2}+1=3*even+1=even+1=odd . Answer: E. If you don't notice this, then one also do in another way. Let x=2k , for some integer k, then: A. \frac{3x}{2}=\frac{3*2k}{2}=3k --> if k=odd then 3k=odd but if k=even then 3k=even . Discard; B. \frac{3x}{2}+1=\frac{3*2k}{2}+1=3k+1 --> if k=odd then 3k+1=odd+1=even but if k=even then 3k+1=even+1=odd . Discard; C. 3x^2 --> easiest one as x=even then 3x^2=even , so this option is never odd. Discard; D. \frac{3x^2}{2}=\frac{3*4k^2}{2}=6k^2=even , so this option is never odd. Discard; E. \frac{3x^2}{2}+1=\frac{3*4k^2}{2}=6k^2+1=even+1=odd , thus this option is always odd. Answer: E. Similar question to practice: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html Hope it helps.

cyberjadugar · Answer

Hi,

Since, x is even we can assume x = 2 or x = 4,
such that x/2 is both odd/even as per the value of x.

Check each option with these values. We get the answer when both x=2, 4 gives an odd value.

Regards,

buymovieposters · Answer

I narrowed this question down to B and E. Based on the rules alone why couldn't it be B?

(3x/2)+1

if x is even then we have an even + odd which would be odd?

thanks for the clarification.

Carcass · Answer

Because the theory is important but also to reach the answer through the most efficient way.

x=2 (as statement says)  OR x=4  (thanks this we know for instance that A is not always true)

\frac{6}{2}  = 3+ 1 = 4   OR 7  (is not always true: one time even one time odd). That's it Same for the other answer choices. You can obtain E in 30 seconds

buymovieposters · Answer

thanks.

certainly i'm trying to answer "odd/even" questions in the most efficient manner possible.

what i would have done on the real CAT is narrowed it down to B and E, then like you let x = 2 or 4 and plugged in to see.

i kind of got tripped up.  typically when we multiply a integer by an even we ALWAYS get an even but (3/2) is frac, therefore multiplying it by an even may or may not make it even?

Bunuel · Answer

That's not correct.

Given that  x  is even, thus  x=2k  for some integer  k . Substitute in option B:

\frac{3x}{2}+1=\frac{3*2k}{2}+1=3k+1  --> if  k=odd  then  3k+1=odd+1=even  but if  k=even  then  3k+1=even+1=odd .

As you can see  \frac{3x}{2}+1  can be even (for example if x is 2, 6, 10, ...) as well as odd (for example if x is 4, 8, 12, ...).

Hope it's clear.

buymovieposters · Answer

thank you for the help.

RR88 · Answer

Option E

x is an Even inetegr. Odd: O, Even: E & Fraction: F

A.  \frac{3x}{2}  =  \frac{3*E}{2}  =  3*E   or   3*O =  E   or   O 
B.  \frac{3x}{2}+1  =  \frac{3*E}{2} + 1  =  3*E + 1   or   3*O + 1 =  O   or   E 
C.  3x^2  =  3E^2  =  3*E  =  E 
D.  \frac{3x^2}{2}  =  \frac{3E^2}{2}  =  3*E  =  E 
E.  \frac{3x^2}{2}+1  =  \frac{3E^2}{2}+1  =  3*E + 1  =  E + 1  =  O

santro789 · Answer

if I take x=2, first option A - would be 3*2/2 = 6/2 =3 and 3 is odd..why is this wrong?

Bunuel · Answer

The question asks which of the following MUST be odd, not COULD be odd. Option A could be odd but it's not always odd while E is odd for any even x.

Hope it's clear.

jfranciscocuencag · Answer

.Hello experts!

I answered correctly this one but after that, I started to think the next doubt:

If 0 is considered an even number...

Then D is not going to become an integer because 0*2 will be 1 so:

(3(1) divided by 2) + 1

What am I doing wrong?

Thank you so much!

Abhishek009 · Answer

Plug in and try to negate -

A.  \frac{3x}{2}

Or,  \frac{3*4}{2} = 6

B.  \frac{3x}{2} + 1

Or, \frac{3*6}{2} + 1 = 10

C.  3x^2

Or,  3*2^2 = 12

D.  \frac{3x^2}{2}

Or,  \frac{3*2^2}{2} = 6

(E) Plug in any number it will always be ODD, Answer must be (E)

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

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

Prep Toolkit

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