(1) x < 8 and x is a positive integer implies that x can take the values 1, 2, 3, 4, 5, 6, 7 but since y = √(9 - x) and y also has to be a positive integer, so the only possible value of x is 5.
If x = 5, y = √4 = 2 (-2 is not possible as y is a positive integer)
So, y = 2.
Hence, (1) is SUFFICIENT to answer the question.
(2) y > 1 implies y can take the values 2, 3, 4, 5, 6, 7...
y = √(9 - x) implies y^2 = 9 - x or x = 9 - y^2
y = 2 implies x = 9 - 4 = 5, a positive integer.
y = 3 implies x = 9 - 9 = 0, not a positive integer.
y = 4 implies x = 9 - 16 = -7, a negative integer.
Similarly, all values of y > 3 will give x a negative value.
So, y = 2, as it is the only one that gives a positive integer value of x.
Hence, (2) is SUFFICIENT to answer the question.
The correct answer is (D).
Rahul Lakhani
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Gurome, Inc.
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