Ultimate Quant Marathon Blog For IIM CAT

Five students Implex, Slam, Sanyo, dewan and nbangalorekar are wearing caps of Blue or Green color without knowing the color of his own cap. It is known that the students wearing the Blue cap always speaks the truth while the ones wearing Green always tell lies. If the students make the following statements

(1) (Implex, Blue) (2) (Slam, Green) (3) (dewan, Blue) (4) at least two of the foregoing (5) none of these

1. Four digits of the number 29138576 are omitted so that the result is as large as possible. The largest omitted digit is (A) 9 (B) 8 (C) 7 (D) 6 (E) 5

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 area of right angle triangle whose inradius is 4 and circumradius
is 10?
a) 28                   b) 56                    c) 96                     d) 192                   e) none of these