is there a quicker way to solve these ds problems?

For the second problem:
2. Is x^y>1?
1. x>1
2. y<1

OA is E

Not sure why this is E. I thought it would be B.

Since Y is less than 1. It can either be
0.....in which case no matter what X is, the result would equal one.
less than 0......in which case no matter what X is, result would be a fraction.
Both results are less than 1. This would answer the problem as in "No"

I'm sure I'm missing something here...

jamesk486 wrote:1. A, B>0, is a^b greater than 10,000?
1. a+b =20
2. b^a>10,000

OA is E
if you put in values it could be the easier but at the same time eyeballing values is risky...is there another way?

2. Is x^y>1?
1. x>1
2. y<1

OA is E

Ques 1

a>0, b>0 a^b >10000 ???

Statement I

a+b=20

a=10, b=10 a^b >10000
a = 1, b =19 a^b <10000

Therefore Insufficient.

Statement II

b^a>10,000

b=10, a=10 a^b>10000
b=100000, a=1 a^b<10000

Therefore insufficient.

Combining I and II

a+b =20
b^a>10000

a=10, b=10 a^b>10000
a=18,b=2, 2^18>10000 but 18^2<10000

Therefore Insufficient.

Hence E is the answer.

Ques 2

https://www.beatthegmat.com/inequality-t16720.html