sandy wrote:

Put y=1 and x=1

Qty A: \(y^x=1^1=1\)

Qty B: \(y^{x+1}y=1^2=1\)

Option C seems correct.

Now put y=2 and x=1

Qty A: \(y^x=2^1=2\)

Qty B: \(y^{x+1}y=2^3=8\)

Here option B seems to be correct.

Now since both cannot be correct thus option D is the best fit.

But the thing is X can never be equal to 1 based on the restrictions given in the problem (i.e. x > 1 and y > 0).

If we do X = 2 and Y = 1:

Qty A: \(y^x=1^2=1\)

Qty B: \((y^x) + 1 = (1^2) + 1 = 2\)

Here the answer is B, but lets keep trying another scenario.

If we do X = 2 and Y = 0.5:

Qty A: \(y^x=0.5^2=0.25\)

Qty B: \((y^x) + 1 = (0.5^2) + 1 = 1.25\)

Here the answer is still B.

If we do X = 2.5 and Y = 0.5:

Qty A: \(y^x=0.5^2.5=0.17677\)

Qty B: \((y^x) + 1 = (0.5^2.5) + 1 = 1.17677\)

Thus the answer is still B. I am really not sure how D could even be answer when Qty B is always greater.