AIMO 2015 Q8

Let $a= \left \lfloor \frac {x}{44} \right \rfloor = \left \lfloor \frac {x}{45} \right \rfloor$

$\underbrace{0≤x≤43}_{44 \text{ values of x}},a=0$

$\underbrace{45≤x≤87}_{43 \text{ values of x}},a=1$

$\underbrace{90≤x≤131}_{42 \text{ values of x}},a=2$

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$\underbrace{1890≤x≤1891}_{2 \text{ values of x}},a=42$

$\underbrace{1935≤x≤1935}_{1 \text{ value of x}},a=43$

So the number of non-negative values of $x=\frac{44×45}{2}=\boxed{990}$ .