All The Best

All the best to all the CAT 2011 aspirants..

Cheers,
Rahul

Problem of the Day 12 Oct 2011

How many factors of  have last digit 2?

Problem of the Day 10 Oct 2011

Ten identical boxes of dimensions  are stacked flat on top of each other, with the orientation of each box being independent and random. If  is the probability that the height of the stack is  and , find . All units are in feet.

Problem of the day 8th oct 2011

Rohan is asked to figure out the marks scored by Sunil in three different subjects with the help of
certain clues. He is told that the product of the marks obtained by Sunil is 72 and the sum of the
marks obtained by Sunil is equal to the Rohan’s current age (in completed years). Rohan could not
answer the question with this information. When he was also told that Sunil got the highest marks
in Physics among the three subjects, he immediately answered the question correctly. What is the
sum of the marks scored by Sunil in the two subjects other than Physics?

(a) 6                  (b) 8                (c) 10               (d) Cannot be determined

Problem of the day 7th Oct 2011

Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books
in such a way that no two books selected by him must have been lying adjacently. In how many
ways can he make the selection?
(a) 56                                (b) 64                           (c) 72                    (d) None of these

Problem of the day 5th Oct 2011

The set S contains nine numbers. The mean of the numbers in S is 202. The mean of the five smallest of the numbers in S is 100. The mean of the five largest numbers in S is 300. What is the median of the numbers in S?

Problem of the day 30 Sept 2011

What is the largest number in the sequence ?




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Problem of the Day 28 Sept 2011

A good approximation of π is 3.14. Find the least positive integer d such that if the area of a circle with

diameter d is calculated using the approximation 3.14, the error will exceed 1.

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Permutations and Combinations- Free Lecture Notes

Many of you have emailed about some easy reference for Permutations and Combinations, Number theory etc. I cannot say if it is an easy reference, but it is one concise one.. It is from one of our Professors at IIT Kanpur, Dr A K Lal, great chap, I must say. This is one gem of a compilation. Hope it helps you.. If the material is too tough, just ignore!

http://home.iitk.ac.in/~arlal/book/mth202.pdf

Enjoy!

Problem of the Day 27 Sept 2011

The diagram below shows some small squares each with area 3 enclosed inside a larger square. Squares that touch each other do so with the corner of one square coinciding with the midpoint of a side of the other square. Find integer n such that the area of the shaded region inside the larger square but outside the smaller squares is √n

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Problem of the day 26 Sept 2011

Let a₁= 2 and a_n+1 = 2a_n + 1. Find the least value of a_n which is not prime.

(a) 47                  (b) 4                    (c) 5                 (d) 95

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Problem of the Day 25 Sept 2011

Let P be the set of all the vertices of a regular polygon of 25 sides with its center at C. How many triangles have vertices in P and contain the point C in the interior of the triangles?


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How to use the options to maximize scores in QA/DI/LR in IIM CAT

The good thing about CAT is, that it is not a mathematics test. So, it helps that you know the process and the steps but you should be smart and try to minimize the work. This is why there are options to help you. A smart use of options will save a lot of time and help you increase your score.

Some examples

Two different two-digit natural numbers are written beside each other such that the larger number is written on the left. When the absolute difference of the two numbers is subtracted from the four-digit number so formed, the number obtained is 5481. What is the sum of the two two-digit numbers?


(a) 70         (b) 71                (c) 72                         (d) 73


Now it is pretty much obvious the number is of the form 55xy
To find xy we can just subtract 55 from the options which gives xy= 15, 16, 17, 18

If you are lucky you will start with 73 and you will know it is right, else even if you start with 15, you will soon reach 18 and get your answer.


The direct method will be a bit long.

 Let n be the total number of different 5-digit numbers with all distinct digits, formed using 2, 3, 4, 5 and 6 and divisible by 4. What is the value of n?

1] 44 2] 32 3] 36 4] 38 5] 40

Permutations & Combinations is probably the most ‘hated’ topic. However, if you understand the basics and use logic, then it is the most fun-filled topic of all. Let us get to this question. As mentioned, we need to find out the 5 digit numbers divisible by 4 formed by the digits given in the question. To be divisible by 4, the last 2 digits should be divisible by 4. So to arrive at the answer, the first step is to find out combinations of the 2 digits from 2,3,4,5 & 6 that are divisible by 4 – eg: 24. Then, for each such combination, the last 2 digits are fixed. The remaining 3 digits can be arranged in 3! Ways = 6 ways. So the answer would be - 6 multiplied by the total no. of combinations of 2 digits divisible by 4. The answer necessarily should be a multiple of 6 and therefore the answer is 36 – option [3]. We just got lucky here, by the way, since there is just one option that is divisible by 6!

Problem of the Day 22 Sept 2011

Susan plays a game in which she rolls two fair standard six-sided dice with sides labeled one through six. She wins if the number on one of the dice is three times the number on the other die. If Susan plays this game three times, compute the probability that she wins at least once.

Problem of the Day 20th Sept 2011

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?


(a) 200   (b) 300 (c) 350  (4) 550

Problem of the day 26.08.09

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

Problem of The day 06.08.09

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

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)?