Both x and y are +ve integers i.e. they shall be 1,2,3,4,5 ...... n

Let us pick up statement #1

(x+y-1)! < 100

Let us write the factorials of 1,2,3,4 and see when does it exceed 100.

1! = 1

2! = 2

3! = 6

4! = 24

5! = 120

So the max value of x+y-1 can be 4 because when it is 5 it exceeds 100.

So x+y-1 = 1,2,3,4 or

x+y = 2, 3, 4, 5

But does not give us 1 solution. Not Sufficient

Let us Pick up Statement #2

y = x^2 -x + 1

This quadratic has no integer solutions, hence we cannot solve it for answer. Not Sufficient

Umm. Combine them replace y from in statement #1 from #2

x+x^2-x+1 = 2,3,4,5

=> x^2+1 = 2,3,4,5

=> x^2 = 1,2,3,4

this will 2 solutions +ve x = 1,2

corresponding +ve y can be 1,3

The answer should be e, the oa is debatable here. please check again.

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