Problem Solving (PS) | Re: If 2^(5x) is an integer, x + 2 = y - 3 and (y^3 - 49y)(y^2 - 7y -18)=0

2^5x is an integer means x mustnot be negative.Also given y-3=x+2, so y=x+5. Hence y is greater than or equal to 5. Calculate values of y. They are 0, 7, -7, 9 and -2. Only 7 and 9 satisfies the condition. So, y=7 and x=2 or y=9 and x=4. xy=14 or 36. xy=14 is in the option and hence the answer.

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