If a is a non-zero integer, is 0

Question

If a is a non-zero integer, is  0 < a^a <1 ?

(1) a < 0

(2) a is even

ElninoEffect · Answer

(1) a < 0
Means a is -ve.
Let's see for a = -1 ; a^a is not greater than 0
But for a = -2 it fits the condition.
Yes and No both are possible.

Not Sufficient.

(2) a is even
For a = 2. It doesn't not satisfies the equation.
For a = -2 It satisfies the equation.
Yes and No both are possible.

Not Sufficient.

Combining we know a is less than 0 and is even.
So it will always satisfy the equation that it will be greater than 0 and less than 1.

Sufficient.

C is the answer.

Solenja · Answer

So basically, The question wasn't asking for a precise value for a?

stne · Answer

Yes you are correct, precise value of  a   is not needed here.

As long as  a  is negative and an even integer then the condition hoids.

If  a   is negative odd , i.e.  -3   then  a^a  becomes:

(-3)^{-3} = (\frac{1}{-3})^3 = \frac{1}{-27} , This is outside the given range.

Well as if  a  is  -2  or any negative even then  a^a :

(-2)^{-2} = (\frac{1}{-2})^2 = \frac{1}{4}   This is within the given range

if  a  is  -4  then  a^a = (-4)^{-4}= (\frac{1}{-4})^4 = \frac{1}{256}  This is also within the given range.

Hence we can see both the statements together given us this info. that  a  is negative even integer.

Hence ans is C

Hope it helps.

If a is a non-zero integer, is 0 < a^a <1? (1) a < 0 (2) a is even