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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Problem of the Day 24 Sept 2011

In triangles ABC and DEF, DE=4AB, EF=4BC, FD=4CA The area of triangle DEF is 360 units more than the area of triangle ABC. Compute the area of triangle ABC



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Problem of the Day 23 Sept 2011

Darryl has a six-sided die with faces 1; 2; 3; 4; 5; 6. He knows the die is weighted so that one face
comes up with probability 1/2 and the other five faces have equal probability of coming up. He
unfortunately does not know which side is weighted, but he knows each face is equally likely
to be the weighted one.

He rolls the die 5 times and gets a 1; 2; 3; 4 and 5 in some unspecified order. Compute the probability that his next roll is a 6.



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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 Week 21 Sept 2011

The leftmost digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either a or b. What is the value of a+b?