abhinav85 wrote:If x is a positive integer.Which of the following must be an odd integer?

A. 3x/2

B.3x/2 +1

C.3x^2

D.3x^2/2

E.3x^2/2 + 1

E

from looking at the choices, you can narrow this down to B and E.

You can do this by recognizing x/2 can be even or odd. (ex. x = 6 or x = 4)

Choice (E) is the only valid option b/c x^2/2 will always give you an even number since its (E*E)/2 = E*O or E*E which = E.

So choice (E) translates to O*E + 1 = E + 1 = O.

The question is not clear.. are we supposed to take only integer part of the number?
in all the options if x is odd, x/2 cannot be an integer..
am i missing something here ?

Sorry but can you explain further how x^2/2 will always give an even result.

ssmiles08 wrote:

abhinav85 wrote:If x is a positive integer.Which of the following must be an odd integer?

A. 3x/2

B.3x/2 +1

C.3x^2

D.3x^2/2

E.3x^2/2 + 1

E

from looking at the choices, you can narrow this down to B and E.

You can do this by recognizing x/2 can be even or odd. (ex. x = 6 or x = 4)

Choice (E) is the only valid option b/c x^2/2 will always give you an even number since its (E*E)/2 = E*O or E*E which = E.

So choice (E) translates to O*E + 1 = E + 1 = O.

mehravikas wrote:Sorry but can you explain further how x^2/2 will always give an even result.

Sure.

We can agree that for a number to be divided by 2, it has to be even.

So even*even = even^2 = even

dividing by 2, will always produce an even number.

There are two possibility when you divide by 2.

For example, (E*E)/2 --->(6*6)/2 = 6*3 (E*O) = E
Another ex, (E*E)/2------>(4*4)/2 = 4*2 (E*E) = E

so either way if you multiply an even number to odd or even number, an even number will always exist.

So this fits into the answer choice perfectly b/c

3*(even) = even;

even + 1 = odd.

-hope this helps.

from looking at the choices, you can narrow this down to B and E.

You can do this by recognizing x/2 can be even or odd. (ex. x = 6 or x = 4)

Choice (E) is the only valid option b/c x^2/2 will always give you an even number since its (E*E)/2 = E*O or E*E which = E.

So choice (E) translates to O*E + 1 = E + 1 = O.

G

Got it man,but tell me one thing that you will treat every expression as a
different expression while solving,like u did in the option E. Every time or just in this case???

3 x x^2/2 +1!!!

abhinav85 wrote:

from looking at the choices, you can narrow this down to B and E.

You can do this by recognizing x/2 can be even or odd. (ex. x = 6 or x = 4)

Choice (E) is the only valid option b/c x^2/2 will always give you an even number since its (E*E)/2 = E*O or E*E which = E.

So choice (E) translates to O*E + 1 = E + 1 = O.

G

Got it man,but tell me one thing that you will treat every expression as a
different expression while solving,like u did in the option E. Every time or just in this case???

3 x x^2/2 +1!!!

I am not sure of what you are asking, but if you look at choice A and B, you can see that they both have the expression x/2 embedded in them.

x/2 can be even or odd ( ex. 6/2 or 4/2)

So A and B can both be counted out b/c they can both result in even integers.

(A) 3* even = even
(B) 3*odd + 1 = odd + 1 = even.

choices C and D can also be eliminated b/c x^2/2 always = even integer.

(C)3*even^2 = even.
(D) 3*(even^2)/2 = even.

(E) will always stand out, since (even^2)/2 = even
3*even = even
even + 1 = odd.

So the last answer choice will always be an odd number.

Hope that helps.

X is positive integer . So X can either be even or be odd

suppose X is divisible by 2

But when you divide EVEN number by 2 you might get an odd number

so the answer is E

abhinav85 wrote:If x is a positive integer.Which of the following must be an odd integer?

A. 3x/2

B.3x/2 +1

C.3x^2

D.3x^2/2

E.3x^2/2 + 1

E

Are you sure the question shouldn't read:

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

If we let x = 1, then for (E) we get:

3(1)/2 + 1 = 1.5 + 1 = 2.5 which is NOT odd.

As the question stands, none of the answers MUST be odd.

Hey Stuart,

I'm sure you mean not even here - 3(1)/2 + 1 = 1.5 + 1 = 2.5 which is NOT odd

Stuart Kovinsky wrote:

abhinav85 wrote:If x is a positive integer.Which of the following must be an odd integer?

A. 3x/2

B.3x/2 +1

C.3x^2

D.3x^2/2

E.3x^2/2 + 1

E

Are you sure the question shouldn't read:

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

If we let x = 1, then for (E) we get:

3(1)/2 + 1 = 1.5 + 1 = 2.5 which is NOT odd.

As the question stands, none of the answers MUST be odd.

2.5 is neither odd nor even (only integers have the property of odd/even). The question is which of the following must be an odd integer, which is why I said "not odd" (some had chosen E as the correct answer, I was demonstrating that it isn't).

mehravikas wrote:Hey Stuart,

I'm sure you mean not even here - 3(1)/2 + 1 = 1.5 + 1 = 2.5 which is NOT odd

Stuart Kovinsky wrote:

abhinav85 wrote:If x is a positive integer.Which of the following must be an odd integer?

A. 3x/2

B.3x/2 +1

C.3x^2

D.3x^2/2

E.3x^2/2 + 1

E

Are you sure the question shouldn't read:

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

If we let x = 1, then for (E) we get:

3(1)/2 + 1 = 1.5 + 1 = 2.5 which is NOT odd.

As the question stands, none of the answers MUST be odd.