answer please

[Inspired]

If x and y are positive odd integers, which
of the following statements could be false?

I. x^y is an odd integer.

II. x^y + x^y is an odd integer.

III. y/x is not an integer.



I only
II only
I and III only
II and III only
I, II, and III

[papgust]

IMO D

I. Odd^Odd will always be an odd integer. This could not be false.

II. 2 * x^y cannot be an odd integer.

III. odd/odd will either result in an odd number or a non-integer.

[ajith]

IMO D

I. Odd^Odd will always be an odd integer. This could not be false.

II. 2 * x^y cannot be an odd integer.

III. odd/odd will either result in an odd number or a non-integer.

just to add on,

take an example where x=1 and y=5

x^y + Y^X = 1+5 =6 is not odd

y/x =5/1 = 5 which is an integer


which proves 2 and 3 can be wrong ....

[Concordio]

x^y + x^y = can be an odd integer. We know that x^y is odd from the first statement and adding two odd numbers can result in an even number.

y/x could be false depending on what numbers you choose.

The answer would be D - II and III only.

[chaitanya.sonavale]

In my opinion, the best way to tackle such questions is "to substitute actual values"

If we assume x=1 and y =3 or vice versa (first two positive odd integers), we can just put those values in the ans options.

[bedazzled]

II is definitely false

x^y will be odd. therefore when we solve this we get x^y(which is odd) + x^y= even

as odd + odd= even

But in case of III we can't say whether it's true or false coz if we do by substitute mehod we get

x=9, y=3 (+ve odd integers)

y/x = 3/9 = 1/3 (not integer)

when value reversed we get
x=3, y=9

y/x =9/3= 3 (integer)

Acc. to me only II is false as III showing ambiguity

IMO B

[harsh.champ]

If x and y are positive odd integers, which
of the following statements could be false?

I. x^y is an odd integer.

II. x^y + x^y is an odd integer.

III. y/x is not an integer.



I only
II only
I and III only
II and III only
I, II, and III

_______________
In the 3rd statement ,suppose x=1 and y=any positive odd integer ,it wil yield y/x as an integer
For statement II , x^y + x^y =2(x^y)......2*any integer is even
**The ambiguity is created by the use of the word "could".........suppose if for the 3rd statement we use x=3,y=5 then 5/3 is not an integer.....so the major testing part of this problem is deciphering what the problem setter demands......going by common sense i would say II and III only