In the xy-coordinate plane, does region bounded by \(x > 0, y < 0, and -y + 2x < 4\) contain point \((a, b)\), where \(a\) and \(b\) are integers ?
Area enclosed by \(x > 0, y < 0, and -y + 2x < 4\) is as attached in the image.
(1)
ab = -4\((a, b)\) can be the following values, as a and b are integers.
\((a, b)=(-1, 4)\) ; \((a, b)=(1, -4)\)
\((a, b)=(-4, 1) \) ; \((a, b)=(4, -1)\)
\((a, b)=(-2, 2)\) ; \((a, b)=(2, -2)\)
All values of \((a, b)\) containing negetive values of x to be eliminated as \(x>0\)
\((a, b)=(1, -4) ; (a, b)=(4, -1)\) and \((a, b)=(2, -2)\) are all located outside the region enclosed by \(x > 0, y < 0, and -y + 2x < 4\)
No values of \((a, b)\) when
ab = -4 are within the region
-Sufficient(2)
a + 4b = 0\(a=-4b\)
\((a, b)=(-4b, b)\)
\(b\) can't be positive integer as \(x\) value can't be negetive because \(x>0\)
values are \((4, -1), (8, -2), (12, -3)\) and so on
all these points are located outside the region enclosed by \(x > 0, y < 0, and -y + 2x < 4\)
No values of \((a, b)\) when
a + 4b = 0 are within the region
-SufficientAnswer : D
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