CAT 2015 Quantitative Ability

x = L.C.M. of (7, 8, 9) - 3 = 504 - 3 = 501
${\mathit{x}}^3+2{\mathit{x}}^2+\mathit{x}-3=\left(\mathit{x}-1\right)\left(\mathit{x}+1\right)\left(\mathit{x}+2\right)-1$
= 500 × 502 × 503 - 1
Remainder when 500 × 502 x 503 -1 is divided by:
11 = 4
3=0
4=3
Required remainder = least possible number which when divided by 11,3 and 4 leaves remainder 4,0 and 3 respectively
Such least no. is 15.