Q16. 
$(AA)^2 = DCBA$, where $A$, $B$, $C$ and $D$ are distinct digits with $B$ being odd. Find the value of $D$. 
A.  4 

B.  6 

C.  1 

D.  1 or 4 
Q17. 
What is the last digit of the number 3^{579}+ 1? 
A.  1 

B.  3 

C.  4 

D.  7 
Q18. 
If $x$ and $y$ are any natural numbers, then which of the following is an odd number? 
A.  $x^y + y^x + (xy)(x^y + x)$ 

B.  $x^y (x + y)(x^y + x)$ 

C.  $y^x (x^y – y) (x^y  x)$ 

D.  None of these 
Q19. 
A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers $111, 222, 333, 444, 555, 666,$ $777, 888$ and $999$?" B immediately gave the desired answer. It was: 
A.  3, 37 and 119 

B.  3, 37 and 111 

C.  9, 37 and 111 

D.  3, 9 and 37 
Q20. 
Two prime numbers $A, B(A < B)$ are called twin primes if they differ by 2 (e.g. 11,13,or 41,43....). If A and B are twin primes with $B > 23$, then which of the following numbers would always divide $A+B$? 
A.  12 

B.  8 

C.  24 

D.  None of these 