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02 Mar 2008, 04:22
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Is product 2*x*5*y an even integer?
1. 2 + x + 5 + y is an even integer
2. x - y is an odd integer
1. 2 + x + 5 + y is an even integer
2. x - y is an odd integer
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02 Mar 2008, 07:45
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Question can be restated as is 5XY (as 2 is already an even number) is even integer or not?
Statment 1:
Implies x + 5 + y => (X+Y) is odd as ODD +ODD = Even (5 is Odd so X+Y has to be Odd)
X+Y can be odd in many ways, even for fractions it will hold true.
So this statement alone cannot answer the question.
Statement 2:
x - y is an odd integer again this can be odd in many ways, even for fractions it will hold true.
So this statement alone cannot answer the question.
Now combine both statements
X+Y = ODD integer and X-Y= Odd integer, again this can be fulfilled by infinite possibilities including fraction.
E.g. X=4.5, Y=3.5 or X=5, Y=4
So this question cannot be answered with these statements.
Answer is E.
Statment 1:
Implies x + 5 + y => (X+Y) is odd as ODD +ODD = Even (5 is Odd so X+Y has to be Odd)
X+Y can be odd in many ways, even for fractions it will hold true.
So this statement alone cannot answer the question.
Statement 2:
x - y is an odd integer again this can be odd in many ways, even for fractions it will hold true.
So this statement alone cannot answer the question.
Now combine both statements
X+Y = ODD integer and X-Y= Odd integer, again this can be fulfilled by infinite possibilities including fraction.
E.g. X=4.5, Y=3.5 or X=5, Y=4
So this question cannot be answered with these statements.
Answer is E.
02 Mar 2008, 07:56
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i get D.
from stat 1, we are told that 7+x+y=even. that means either x is even and y is odd, or vice versa. they cant both be even or both be odd.
now, regardless of which is even and which is odd, 2x5y will always be even. (2x) will always be even, because you either have even x even = even, or even x odd = even. For 5y, you have either odd x even, or odd x odd, which gives odd or even, but when multiplied by the even result from 2x, you always get an even number.
from stat 2, x-y=odd. again, x can be odd/even, and so can y. same situation as above. suff.
from stat 1, we are told that 7+x+y=even. that means either x is even and y is odd, or vice versa. they cant both be even or both be odd.
now, regardless of which is even and which is odd, 2x5y will always be even. (2x) will always be even, because you either have even x even = even, or even x odd = even. For 5y, you have either odd x even, or odd x odd, which gives odd or even, but when multiplied by the even result from 2x, you always get an even number.
from stat 2, x-y=odd. again, x can be odd/even, and so can y. same situation as above. suff.
