Ultimate Quant Marathon Blog For IIM CAT

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

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

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

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

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

In 1896 lord Coin has decided to play a game. From the January 1 till December 31 every day he chooses among two match boxes an arbitrary one and placed a match from it to another box (if the chosen box was not empty). If the chosen box was empty then he placed a match from
the other box to the chosen one. What is the probability that after the December 31 the both boxes will have an equal number of matches if at the beginning each box had a) n = 400 b) n = 200 c) n = 100 matches?

Find the number of solutions in distinct positive  integers of x^4+y^4=z^4

A) 0                 B) 1                  C) 2                         D) 3                E) More than 3

Given that 1025/1024=1.0009765625, find the sum of the digits of 5¹⁰?

(a)  36       (b) 40    (c) 50   (d) 102   (e) 41

On a circle 26 equidistant points are marked. these points are joined to form a triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides.?

A) 318 B) 312 C) 288 d) 624 e) None of these