If r and s are positive integers, and r2 + r/s is an odd integer,

Question

If r and s are positive integers, and  r^{2} + r/s  is an odd integer, which of the following cannot be even?

A. 3r + 2s

B. (r-1)(s+2)

C. r^{s+1} + s^r

D. r^{3} +3

E. s^{4} +4

nailin16 · Answer

it can be B too...
why not B

Posted from my mobile device

Tridhipal · Answer

Hi,

Question is asking about "which of the following  CANNOT  be   EVEN  ".

Option B is always even. So this is not the answer

Hope it clarifies !

umangsharma94 · Answer

how can r^2+r/s be an odd positive integer at first place? just wondering!

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niks18 · Answer

r^{2} + \frac{r}{s}=Odd , So there are two scenarios -

Case 1:   r^2=Odd  and  \frac{r}{s}=Even . Now if  r  is  Odd  then  s  has to be  Odd  and  \frac{Odd}{Odd}  cannot be  Even . Hence this case is invalid

Case 2:   r^2=Even  and  \frac{r}{s}=Odd

=>s*Odd=r=Even . hence  s  has to be  Even .

Now looking at the options only Option  D  cannot be even because Option  D  translates into

Even+Odd=Odd

Option  D

niks18 · Answer

Hi  umangsharma94

yes it can be

for eg. if r=s=2, then the equation becomes 4+1=5=odd

niks18 · Answer

Hi  nailin16

first you need to ascertain the property of  r  &  s  here. Once you know that both are Even then Option B translates into -

(even-odd)*(even+even)=even

umangsharma94 · Answer

Yeah, i actually got it a bit late after I replied! Thanks

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GyMrAT · Answer

Given  r^{2} + r/s  - is an Odd Integer

implies that  r/s  is odd &  r  is even, since Odd/Even cannot be an integer.

Hence Answer D.  r^{3} +3  cannot be even.

Thanks,
GyM

bumpbot · Answer

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If r and s are positive integers, and r2 + r/s is an odd integer,

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