Q11. 
A certain number when divided by 222 leaves a remainder 35, another number when divided by 407 leaves a remainder 47. What is the remainder when the sum of these two numbers is divided by 37? 
A.  8 

B.  9 

C.  12 

D.  17 
Q12. 
Find the remainder when $2^{31}$ is divided by $5$. 
A.  4 

B.  5 

C.  3 

D.  7 
Q13. 
The sum of three digit number is subtracted from the number. The resulting number is always: 
A.  divisible by 6 

B.  not divisible by 6 

C.  divisible by 9 

D.  not divisible by 9 
Q14. 
If $N=2^3×3^4$ , $M= 2^2×3×5$, then find the number of factors of $N$ that are common with the factors of $M$. 
A.  8 

B.  6 

C.  18 

D.  20 
Q15. 
The remainder when the positive integer $m$ is divided by $7$ is $x$. The remainder when $m$ is divided by 14 is $x + 7$. Which one of the following could $m$ equal? 
A.  45 

B.  53 

C.  72 

D.  85 