Quote:
X and Y are the lengths of two non-hypotenuse sides of a right triangle, is the area of the triangle an integer?
(1) X is a prime number.
(2) Y is an odd integer.
Area = 1/2(LxB) = 1/2 (X x Y)
Statement 1) X is a prime no. i.e 2,3,5,7,11 and so on. Except for 2 all prime no.s are odd.
If X=2 => Area=1/2(2xY) = Area = Y ... We dont know whether Y is an integer or not - Insufficient.
Statement 2) Y is an odd Interger ... We dont know whether X is an or not - Insufficient.
Statement 1) & 2) combined
Area = (Prime no. x Odd no.)/2
If X = 2 => Area = (2 x Odd no.)/2 => Area = Odd Integer ... True
If X = 3,5,7 and so on for prime no. => Area = (Odd x Odd)/2 = Even/2 .. Not true
Choice E) is the correct ans. Statement 1) & 2) combined are not sufficient to ans the question.
Good luck
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