Management Aptitude Test 2016 Paper

(b) Let the number be x
According to the question,
x = 17 ${\mathit{q}}_1$ + 12
Also. x = 11 ${\mathit{q}}_2$ + 8
⇒ 17 ${\mathit{q}}_1$ + 12 = 11 ${\mathit{q}}_2$ + 8
⇒ 17 ${\mathit{q}}_1$ -11 ${\mathit{q}}_2$ = - 4
⇒ 11 ${\mathit{q}}_2$ -17 ${\mathit{q}}_1$ = 4
The above equation is satisfied when ${\mathit{q}}_2$ = 5 and ${\mathit{q}}_1$ = 3.
Now, x = 17 ${\mathit{q}}_1$ + 12
= 17 x 3 + 12
= 51 + 12 = 63
When 63 is divided by 23, then the remainder is 17