Problem 1:
If a, b, c, and d satisfy the equations
then what is the numerical value of ?
Problem 2:
Suppose x and y are positive integers with and
and
when divided by 5, leave remainders 2 and 3, respectively. It follows that when
is divided by 5, the remainder is necessarily equal to
(A) 2
(B) 1
(C) 4
(D) none of the foregoing numbers
Problem 3:
The number of different solutions of the equation
, where each of x, y, and z is a positive integer is
(A) 36
(B) 121
(C)
(D) , which denote binomial coefficients
Problem 4:
The hands of a clock are observed simultaneously from 12.45 pm onwards. They will be observed to point in the same direction some time between
(A) 1:03 pm and 1:04 pm
(B) 1:04 pm and 1:05pm
(C) 1:05 pm and 1:06 pm
(D) 1:06 pm and 1:07 pm.
More later,
Nalin Pithwa