Some basic DI tools

Here are some really basic tools to help you make calculations faster. I am not including the usual "vedic math" or "speed calc" techniques. I found that simpler methods help more!

I am sure you are all aware of that ubiquitous formula (a+b+ab/100). But I am equally certain that you (or even me, for that matter) have discovered even half of the uses of this formula. Well, for now, lets focus on its use in division.

As a really simple starter, lets take a division question:

If 1/3 = 33.33%, what is 1/2? Obviously, its 50%, silly! So, what does it have to do with that formula? Here's what:

Apart from its more popular uses like successive discounts etc, this formula holds true for ANY product of two or more quantities. In fact, this is the most generalized use of the formula. If P=AxB, then an change of a% in A and b% in B will result in a change of (a+b+ab/100)% in P. Conversely, if P has to remain constant, an a% increase/ decrease in A will necessitate a corresponding change of a/(100+a)% or a/(100-a)% in B respectively.

Now,
1/3=33.33% can also be written as 1=3 x 33.33% and
1/2=50% can also be written as 1=2 x 50%.

So, the product has remained constant at 1. 3 has decreased to 2. That's a decrease of 33.33%. According to the formula, the other factor will increase by 33.33/(100-33.33)= 50%. So, 33.33% will increase by 50% to 50%.

This may sound too obvious and easy, but take a look at what you can do with this. How would you calculate, say, 113/256? Now, we know that 113/226 = 1/2=0.50. Using this fact, we can calculate the deviation from 0.5. Since 256 is 30/226 or roughly 1/7.5 or 2/15 or 13.33% more than 226, it means that the final result will be 13.33/(100+13.33)% less than 0.5. That is, approx. 12% less than 0.5, or 0.44. That is fairly close to the correct answer that is 0.4414!

Even if you had taken 13% (instead of dividing it by 113.33), you would have been quite close at 0.45! The key is to round off the denominator to a "convenient" number. And if your denominator deviation is not more than 15%, you can simply take this same deviation as correction in your answer. To summarize, follow these steps:

1. Round off the denominator to either a multiple/ factor of the numerator, or to the nearest hundred. This way, the calculation will be easier for the new fraction.
2. Calculate the percentage deviation from the actual denominator. You may use approximations depending on the need of the hour.
3. Provided that the percentage deviation is less than 15%, adjust your answer by the same percentage in the "other direction".

Obviously, this involves a fairly high amount of calculation, but the good news is that it will get easier with a better knowledge about percentages.

Why don't you go ahead and try out the following:

135/283=? (Hint: Take 283 as 270 or 300)
178/1327=? (Hint: Take 1327 as 1300)

Collaborate, not Compete!

An Indian Express article this week by Bihar's Additional Director-General of Police Abhyanand, 55, who teaches physics at Bihar's Super-30 Institute for IITJEE caught my attention. If you are not keyed into the news, this institute run by Abhyanand and Anand Kumar, 36, a local mathematician, takes up select students from the minority classes. They are taught for the IITJEE exam, arguably the toughest exam of its kind in the world. All of this comes free-of-cost!

The results this year: 30 students of this institute were ALL selected for the famed IITs! (Read the full story here)

I was always a keen admirer of this venture, but what came as a bit of a surprise was the fact that these 30 students were actually helping each other in their preparation. As far as I remember my days of preparation, I never saw two students preparing together for IITJEE! There were situations when friends used to hide their progress from each other, as if there was only one seat in IITJEE, and they were the two finalists! And here were a bunch of brilliant students, who actually helped each other towards the common goal.

When I look at the MBA (read CAT) preparation at our centre, I am relieved that there are groups getting ready for the test, NOT individuals. We have always believed that 5 brains working together is always better than the five working in isolation. At CL, Pune, we don't have as many number of students as there are total number of seats in all the IIMs put together! Well, theoretically, every student here stands a chance to grab an IIM seat :-)

The Bottomline: Form groups of 4-6 friends=> Spend all the time you can afford with each other (mainly studying, and hence, at the centre)=> Get into the IIMs with the same group as your batchmates!

Enjoy!

SAAT SAMUNDAR PAAR...(MIGRATORY WORDS)

I don't know why they do it? Now look at the word MODUS OPERANDI: It simply means a method of operating or functioning. It is a Latin word. You will see that ,this is a word often associated with any burglary or even murder sometimes. The synonyms are routine, a process, a method. But seriously, why do the authors do it? Why couldn't they have used the simple words? This makes me ponder about the incentive attached to being so verbose. Is it that they want to impress their readers? Or be the center of their attention or just that they are a bunch of sadist who enjoy imagining the perplexed expression on their readers' face.
Like tough English words were not enough!!!!!!!!!! The rampant use of foreign words is definitely not going to let us breathe easy. Can we fight this? Not Really. Like they say if you can’t fight them, join them. No guys I wouldn't like to join the much hated league. On the other hand, your very own AGONY AUNT is right here, trying to placate the pain of mugging up new words. Before they take a toll on you, let's conquer them.
Hence I would keep updating you with the new foreign words. Other commonly used foreign words are:
Penchant (French) means a strong inclination, taste or liking for something. Panache (French) means Dash and Flamboyance, Style. Aficionado (Spanish) means an ardent devotee. Bete Noire (French) means something or someone particularly disliked. Dolce Vita (Italian) just means sweet life .Faux pas (French) is a social blunder. Schadenfreude (German) is a person who derives pleasure at someone's distress. In situ (Latin) means situated in the original or natural position and Quid pro quo (Latin) means something for something, equal exchange.
OK…signing off for now…will be back soon with more GENRE of words.....

OOPS I DID IT AGAIN(CONTINUED)

Guys, here I come again with the common confusables. As i had said earlier CAT-07 showed particular affinity towards these word pairs and XAT -2008 too followed suit. Here are few more word pairs to add to your kitty :)
6.(a)loathe(v)-hate or dislike something.
(b) loath(v)-unwilling, reluctant.
7(a) tortuous(adj)- full of twists and turns, lengthy.
(b) torturous(adj)-characterized by pain.
8(a)Censor(n)-1.an official who examines books, plays, news reports, motion pictures, radio and television programs, letters, cablegrams, etc., for the purpose of suppressing parts deemed objectionable on moral, political, military, or other grounds. (snip, snip, cut, cut:)....)
2.any person who supervises the manners or morality of others.
(b) censure(v)- to criticize strongly
9(a)Endanger(v)-expose to harm or danger.
(b) Engender(v)-to cause or to produce.
10(a) connive(v)-to cooperate secretly, conspire.
(b) convivial(v)-Friendly, agreeable.
Well , i dont want you guys to suffer from OD[overdose:) ] thats all for now..vocabulary becomes effectively enhanced only when you keep going back to the words. In other words, revision is the only way that will equip you better.....

Vocabulary

Well I seriously seem to be spending a lot of time with the letter "G".Many of us are confused with the pronunciation of some words beginning with G as sometimes it takes the phonetics of 'Guh' as in GAIN, or 'Juh' as in GIST and even worse is the pronunciation with "Zhuh" as in GENDARME(zhendaarm) which refers to a member of the French Police.The only good thing about it is that the 'Zhuh' sound is generally for the Foreign Words.
Here is a double dose of words with 'G'--- "Grandiloquent"( "GRAND" + "ELOQUENCE") which means using long or complicated words to impress people.Then there is "Ghoul"('gool') which means a person who revels in what is morbid,loathsome or filthy.

Will try my best to concentrate on a different letter the next time!

Vocabulary

I am back with some more inspirations from Greek and Roman Mythology.This time i have got a phrase that i assume many of us have heard befoer...it's called "The Gordian Knot" which means a very difficult or impossible task or problem.Legend has it that King Gordius tied a very complicated knot and said whoever undid it would become the ruler of Asia.Alexander the great cut though the knot and the rest is history.
Well as always I could not help but connect it to the Swayamwara ceremony of Sita in which Rama broke the Bow which no one else could and went on to marry the princess.
Somehow all this proves that somewhere the mythology from different parts of the world confluences to a particular point.
Well let's get more inspired and improve our vocabulary!