QuantoLogic: IIM

Showing posts with label IIM. Show all posts

Saturday, August 5, 2017

Problem of the week 6th August 2017

ABC is a right angled triangle with hypotenuse AC such that a circle of radius 6 passes through B and C. Th circle cuts the side AB and AC at points D and E respectively such that AD=5 and AE=4. Find BC

Tuesday, April 24, 2012

My IIM Interview Experience

X: Hi come on, have a seat.
me: Thank you Sir.
Y: SO are you from Bombay or Jharkhand?
me: Sir, I am from Jharkhand currently based in Bombay.
Y: Oh nice, Ranchi is a beautiful place. Been to Ranchi?
me: Yes Sir it is.
X: So you are a Jha from Jharkhand?
me: Yes Sir.
X: So you guys so big in Jharkhand, that they name the whole state after you?
(laughter all around)
Me: Not exactly Sir. Jharkhand means the land of forests, it has nothing to do with us 'Jhas'.
X: Is it? I thought it was the land of Jhas. So you are not a Jha because you are from Jharkhand?
Me: No Sir. I was a Jha even before Jharkhand was called Jharkhand.
(laughter all around)
X: Man, I am confused now.Jha not from Jharkhand, Jharkhand not from Jha.So where are Jhas from?
Me: Sir Mithila.
X: Any famous person from Mithila?
Me: Sir, Goddess Sita. She was called Maithili as she was the princess of Mithila.
X: She is from mythology. Any other?
Me: Sir, Prakash Jha, Udit Narayan.
X: They are from bollywood. Any other?
Me: Sir, Jagannath Mishra. He was the CM of Bihar who built the famous Mahatma Gandhi Setu on the Ganga River near Patna.
X: Nice, any more?
Me: Sir, Lalit Narayan Mishra. he was the railway minister of India in 1970s. He was killed in a bomb blast when inaugurating a railway station in Bihar.
X: Can you name the station where the bomb blast happened?
Me: I am not sure, but I can take a guess if you allow me.
X: Hmmm, ok take a guess.
Me: Samastipur?
X: That's right. How did you guess that?
Me: Samastipur is one of the largest stations in North Bihar. And railway penetration in 70s was very less in Bihar. So I guessed it.
X: You guessed it or you knew it?
Me: Sir, I was confused between Hajipur and Samastipur. I guessed Samastipur.
X: Ok. Any more?
Me: Pardon me Sir.
X: Any more famous people from Mithila?
Me: Sir, I do not remember the full name but Prof D N Jha from DU is quite famous.
X: Is he famous or controversial?
Me: I think famous as well as controversial.
X: What is the controversy surrounding him?
Me: Sir, I don't remember what controversy it was exactly.
X: Do you know what he teaches?
Me: Sir, he teaches History. Rather he was the head of the history department of DU.
X: Nice, so you know about him. How do you know about him?
Me: Sir I had a discussion about his book with my brother-in-law in 2001. My brother in law also teaches history in DU colleges.
X: So you remember everything discussed in 2001? Sharp memory you got.
Me: Thank You sir. But it will be wrong to say that I remember everything. If I did, I would remember the controversy as well.
(laughter all around)
X: Ok. Now we will ask something else where you do not need your memory.
(laughter all around)
Me: Ok Sir

X: Prof D N Jha was recently involved in a vey famous case. Can you guess which case?
Me: Sir, I am not sure. I can take a guess.
X: I asked you to guess only. Do it.
Me: Babri Masjid case in the Allahabad High court.
X: Impressive, how did you guess that?
Me: I could only think of one famous case where opinions of historians was needed.
X: Right. He was one of the four independent historians consulted by the High Court.
Me: Right Sir.
X: What do you want us to ask you?
Me: Sir anything.
X: You think you can answer everything?
Me: No Sir. I meant it is difficult for me to choose.
X: So you don't know what you know?
Me: No Sir. I am very sure what I know and what I don't know.
X: Ok tell me what should we ask you then?
Me: Maths.
X: No. We have given you the rubiks cube to test that.
(laughter all around)
ME: books, football maybe.
X: Ok we will ask about both of them. You are free right?
Me: Excuse me Sir?
X: I mean you are not getting delayed or something. You don't have any appointment or anything?
Me: No Sir, I am totally free. No appointments for today.
(laughter all around)
X: Good.
The interview continued towards books, football and general HR questions.
Y and Z didn't ask anything. X was the one who asked everything.

Friday, October 21, 2011

All The Best

All the best to all the CAT 2011 aspirants..

Cheers,
Rahul

Wednesday, October 12, 2011

Problem of the Day 12 Oct 2011

How many factors of $2010^{2010}$ have last digit 2?

Monday, October 10, 2011

Problem of the Day 10 Oct 2011

Ten identical boxes of dimensions $2 \times 3 \times 5$ are stacked flat on top of each other, with the orientation of each box being independent and random. If $\frac{m}{n}$ is the probability that the height of the stack is $31$ and $\gcd(m, n)=1$ , find $m$ . All units are in feet.

Sunday, October 9, 2011

Problem of the Day 9th Oct 2011

In an increasing Arithmetic Progression, the product of the 5th term and the 6th term is 300. When
the 9th term of this A.P. is divided by the 5th term, the quotient is 5 and the remainder is 4. What is
the first term of the A.P.?
(a) 12 (b) –40 (c) –16 (d) –5

Saturday, October 8, 2011

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

Friday, October 7, 2011

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 6th Oct 2011

If xΔ(y +1) = yΔ(x +1), xΔ x = 1 and (x − y)Δ(x + y) = xΔ y, then what is the value of 1001Δ1?
(a) 1000 (b) 100 (c) 10 (d) 1

Wednesday, October 5, 2011

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?

Tuesday, October 4, 2011

Problem of the Day 4th Oct 2011

Find $x$ and $y$ , where the variables are natural numbers:

$\frac{xy + y}{x + y} = \frac{15}{7}$
$\frac{x^2 + y}{2x + y} = \frac{19}{11}$

Monday, October 3, 2011

Problem of the Day 3rd Oct 2011

How many ordered pairs of positive integers $(m, n)$ satisfy the system

$\begin{align*}\gcd (m^3, n^2) & = 2^2 \cdot 3^2,\\ \text{LCM} [m^2, n^3] & = 2^4 \cdot 3^4 \cdot 5^6,\end{align*}$

where $\gcd(a, b)$ and $\text{LCM}[a, b]$ denote the greatest common divisor and least common multiple of $a$ and $b$ , respectively?

(A) 0 (B) 1 (C) 2 (3) More than 2

Sunday, October 2, 2011

Problem of The day 2nd Oct 2011

Let [x] and {x} respectively denote the integer and fractional part of of a real number x. If {n} + {3n}=1.4, find the sum of all possible values of 100{n}.

(A) 180 (B) 145 (C) 85 (d) 102

Saturday, October 1, 2011

Problem of the day 1 oct 2011

In 3-dimensional space, there are 3 rays leaving point $P$ . Any pair of 2 rays make a 60 degree angle with each other in their respective planes. Points $A$ , $B$ , and $C$ are situated on the rays (one per ray) such that $PA$ , $PB$ , and $PC$ are all integers, and $PA<PB<PC$ . if $PC=2010$ and $PB$ is odd, then determine the value of $PA$ if $\angle ABC = 90^{\circ}$ .

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Friday, September 30, 2011

Problem of the day 30 Sept 2011

What is the largest number in the sequence $\sqrt{50},2\sqrt{49},3\sqrt{48},\cdots,49\sqrt{2},50$ ?

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Thursday, September 29, 2011

Problem of the Day 29 Sept 2011

Let a, b, c be three distinct odd natural numbers. Which of the following can be the sum of the squares of a, b and c?

(a) 3333 (b) 5555 (c) 9999 (d) 7777

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Wednesday, September 28, 2011

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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Tuesday, September 27, 2011

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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Monday, September 26, 2011

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