SSC Selection Post 2022 PYQ — Question 56

The correct answer is option 2 i.e. 11. 

Let the resultant number be 'p',

$\Rightarrow p = 53^3 - 7 \times 57 \Rightarrow p = (55 - 2)^3 - (7) \times (55 + 2)$

$\Rightarrow p = (55^3 - 8 - 3 \times 55^2 \times 2 + 3 \times 55 \times 2^2) - 55 \times 7 - 14$

$\Rightarrow p = (55^3 - 6 \times (55)^2 + 12 \times (55) - 7 \times (55) - 8 - 14$

$\Rightarrow p = (55^3 - 6 \times (55)^2 + 12 \times (55) - 7 \times (55) - 22$

$\Rightarrow p = 11[5 \times (55)^2 - 6 \times (55)^2 + 12 \times (55) - 7 \times (55) - 22]$

The common factor in resultant number is 11, hence the number is divisible by 11