Problem of the Day 30.07.09

Find the sum of the digits of the least natural number N, such that the sum of the cubes of the four smallest distinct divisors of N is 2N?

1)  9                                2) 8                             3) 7                    4) 6                      5) 10

Bonus QUestion 28.07.09

Suppose K be the number of integers n such that (2^n+1)/n^2 is also an integer.
Then K is
a) 0               b) 1               c) 2              d) 3              e) none of these

Problem of the day 28.07.09

if a<b and 12²+4²+5²+3²=a²+b² the find (a+b)?

Problem of the day 27.07.09

Find the number of quadratic polynomials ax² + bx + c such that:

a) a, b, c are distinct.

b) a, b, c ε {1, 2, 3, ...2008}

c) x + 1 divides ax² + bx + c
a) 2013018            b) 2013021            c) 2014024             d) 2018040       e) none of these

Bonus Question 26.07.09

The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area?
(A) 75 (B) 144 (C) 150 (D) 300 (E) none of these

Problem Of the Day 26.07.09

If x² + y²= 1 and x, y are real numbers. Let p, q be the largest and smallest possible
value of x + y respectively. Then compute pq
a) 0                    b) 1/2         c) −1/2                          d) 2                           e) −2