VJesus12 wrote:If x and y are positive integers such that x^2+y^3 is a prime number less than 18, what is the value of y?
(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number
Perfect squares less than 18:
1, 4, 9, 16.
Perfect cubes less than 18:
1, 8.
Options for x²+y³ such that the sum is prime:
1+
1 = 2, implying that x=1 and y=1.
4+
1 = 5, implying that
x=2 and y=1.
9+
8 = 17, implying that
x=3 and y=2.
16+
1 = 17, implying that x=4 and y=1.
Both statements are satisfied by the two green cases above:
x=2 and y=1, with the result that x²+y² = 5 and x²-y² = 3.
x=3 and y=2, with the result that x²+y² = 13 and x²-y² = 5.
Since y can be different values, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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