Ultimate Quant Marathon Blog For IIM CAT

Problem of the day 26.08.09

Implex — Wed, 26 Aug 2009 06:51:53 +0000

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

Implex: I see 3 blue caps and one Green
Slam: I see 4 Green caps
Sanyo: I see 1 Blue cap and 3 Green
dewan: I see 4 Blue caps

Then, which among the following (Student, Cap Color) combination is correct?

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

Tagged: cat, CAT 2009, IIM, Logic, Online CAT, quant

Problem of The day 06.08.09

Implex — Thu, 06 Aug 2009 10:42:10 +0000

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

Tagged: cat, CAT 2009, IIM, Number Theory, Online CAT

Problem of the Day 30.07.09

Implex — Thu, 30 Jul 2009 13:03:12 +0000

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

Tagged: cat, IIM, Number Theory, Online CAT

Bonus QUestion 28.07.09

Implex — Tue, 28 Jul 2009 14:43:42 +0000

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

Implex — Mon, 27 Jul 2009 20:28:57 +0000

if a

Tagged: Algebra, cat, CAT 2009, IIM, Mock Cat, Mock Quant, Number Theory, Online CAT, quant

Problem of the day 27.07.09

Implex — Mon, 27 Jul 2009 07:50:06 +0000

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

Tagged: Algebra, cat, CAT 2009, IIM, Mock Cat, Mock Quant, Number Theory, Online CAT, quant

Bonus Question 26.07.09

Implex — Sun, 26 Jul 2009 11:20:18 +0000

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

Tagged: cat, CAT 2009, Geometry, IIM, Online CAT, Problem of the week

Problem Of the Day 26.07.09

Implex — Sun, 26 Jul 2009 07:08:25 +0000

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

Tagged: Algebra, cat, CAT 2009, IIM, Mock Cat, Mock Quant, Problem of the week, Problems, trigonometry

Problem of the day 25.07.09

Implex — Sat, 25 Jul 2009 15:42:47 +0000

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?

Tagged: cat, CAT 2009, IIM, Problem of the week, quant

Bonus Question 16.07.09

Implex — Thu, 16 Jul 2009 15:27:44 +0000

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

Tagged: Algebra, cat, CAT 2009, IIM, Mock Cat, Mock Quant, Number Theory, Online CAT