csat-suneung 2006 Q8

csat-suneung · South-Korea · csat__math-science 3 marks Inequalities Integer Solutions of an Inequality

For two natural numbers $a , b ( a < b )$, the fractional inequality
$$\frac { x } { x - a } + \frac { x } { x - b } \leqq 0$$
is satisfied by exactly 2 integers $x$. What is the number of ordered pairs $( a , b )$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

For two natural numbers $a , b ( a < b )$, the fractional inequality

$$\frac { x } { x - a } + \frac { x } { x - b } \leqq 0$$

is satisfied by exactly 2 integers $x$. What is the number of ordered pairs $( a , b )$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5

Paper Questions

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