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Friday, December 30, 2011

The Year End Rigmarole

Another year comes to a close . I often wonder over the dichotomy of 'time'.
There are days when I count each hour and minutes and time seems to on a standstill , and then there are months ,years that are over in a jiffy.


Some typical year-end shenanigans:

1)Early morning eye  defying fog .


2)The reluctant bather.I gather there are many others in this breed(me included)
3)The 'Blanket Ban' on cold coffee.
4)The Summer in Australia.Boxing day and New Years Test on 2 Jan




5)Best of the year gone by snippets in newspapers,magazines

6)New Year Resolutions
7) The early morning walks at Old Delhi.

8)The Auto Expo at Pragati Maidan


9)The abominable position that the less fortunate find themselves in




The list goes on ...

Over to 2012.

Tuesday, October 11, 2011

Sentence Correction : Demystified

In this article, I will try to highlight the various types of errors that one may encounter in a sentence correction problem (which may include selecting the correct/incorrect sentences in the exam)
Remember, more often than not, a sentence correction question will present you with a combination of several errors at once. They must all be corrected, and no other errors must be introduced. The following sections deal with the different errors separately, but the example questions may present you with multiple errors. So, be careful!
Here are the most common errors in sentences.
1. Using the wrong word.
2. Singular-Plural pronouns.
3. Modifier errors
4. Parallelism errors
5. Idiomatic errors.
6. Diction errors
7. Punctuation errorsSentence Correction image 4
Let us have a detailed look at them now.

1. Using the wrong word

• Practice vs. Practise
• Affect vs. Effect
• Lay vs. Lie
Practice vs. Practise
These words sound alike and are spelled similarly – they differ only by one letter. They have a variety of meanings (to practise an instrument, a profession; a doctor’s practice etc.) but there is one golden rule:
The word practise with an S is a verb, whereas the word practice with a C is anoun.
For example: I practise the piano (verb), but I did my piano practice (noun). The doctor practised for twenty years (verb), but his brother, the solicitor, had a practice that lasted over thirty years.
Another pair of words that functions exactly the same way is advise (the verb) and advice (the noun).

2. Singular-Plural Errors

Illustrative Sentences
• A picture of the All-Star Team, composed of players from different leagues, were given to each member.(This is incorrect)
Explanation
The trick to catching these errors is to isolate the true subject of a sentence. Remember to use the bracket technique to isolate the distracting phrases so that you can focus on the important elements of each sentence.
In the above example, the subject—picture—is singular, but the verb—were—is plural.
Therefore, this is not a correct sentence. The correct statement would be:
A picture of the All-Star Team, composed of players from different leagues, was given to each member.

3. Modifier Errors:

Modifiers should be close to what they modify. This is the golden rule used for finding modifier errors.
Example: The man saw the house on the hill with the telescope.
So, why is this wrong?
We have two modifiers here, which are phrases that give additional information: on the hill and with the telescope. It isn’t clear from the way in which the sentence has been corrected to what these modifiers refer. We can reasonably assume that the seeing was done with the telescope, since that is what telescopes are for. Probably, the house was on a distant hill, so it seems the scenario on the left is the most likely one. However, it would have been better to put the modifier with the telescope next to the seeing, and the on the hill next to the house:
The man saw with the telescope the house on the hill.
… or better still …
Using the telescope, the man saw the house on the hill.
This makes it abundantly clear that the seeing was done with the telescope, and it is a quite legitimate change to make.
For more on Modifiers, read this article on Modifiers: Misplaced Modifiers and Dangling Modifiers.

4. Parallelism Errors

Parallelism is the comparing or listing of two or more phrases or clauses which should both/all take the same form. Here is an example of two parallel items being compared:
Seeing is believing.
In this case, seeing is being listed alongside believing. They both take the same form, i.e. a verb ending in “-ing” which is being used as a noun (termed a gerund in grammatical text books). The three-word proverb above does not contain any parallelism errors. We could also rewrite the proverb as follows:
To see is to believe.
This time, both verbs are listed as infinitives, “to …” Again, since they are both in the same form, there is no parallelism errors. However, if we wrote the following, it would be wrong:
To see is believing.
Here a gerund is being compared to an infinitive. This is grammatically wrong. The same applies to the following:
Seeing is to believe.

5. Idiom Errors

The idiom errors arise due to incorrect usage of idioms. It is not easy to spot these errors if one hasn’t heard of them before. Go through the various idioms booklets for practice.
Sample this:
• Many teenagers feel a great deal of pressure to conform with the values, attitudes, and behavior of their peers.(Incorrect idiomatic usage).
The correct expression is “conform to”; the preposition “with” is incorrect.

6. Diction Errors

A diction error is using the wrong word for the meaning intended. You have to be very careful to spot this error because the word in the sentence is spelled almost exactly like the word that should have been used.
Example:
• The space launch will take place next month, providing that the weather is good.
The word providing in the example should have been provided. A diction error is not a spelling error, but rather the wrong word.

7. Punctuation errors

Sentence fragments and run-on sentences can be fixed with proper punctuation and by transitional words or phrases.
• Example:
Many students are intimidated by math, they do not realize that solving problems is a lot like following simple recipes.
The error here lies with the comma that appears after the word math.
Why is it an error?
When two halves of a sentence can both stand on their own, a comma is not the correct punctuation. The comma here should be replaced by either a period or a semicolon.
So, replace the comma with a semi colon in the above statement and you are done.
Lets take a look at another common error.
Example 2:
The summer program offered intensive immersion sessions in the following languages, French, German, Spanish, Italian, Russian, Korean, Chinese, Japanese, and even Latin and ancient Greek.
The statement looks just about fine. I can’t find any tense, modifier, parallelism error in it.
The error lies in the incorrect punctuation (read absence of a colon) in the sentence. The error free sentence should be:
The summer program offered intensive immersion sessions in the following languages: French, German, Spanish, Italian, Russian, Korean, Chinese, Japanese, and even Latin and ancient Greek.
Important: A colon is used to introduce specific information discussed earlier in a sentence.
These are few of the major errors that you will encounter in the exam. Solving sentence correction questions from previous year papers is the only panacea for gaining a sufficient level of prowess over it.

Monday, September 12, 2011

Finding remainders using Euler's theorem


This method is very useful when the divisor and dividend are relatively prime numbers...

step 1: To calculate euler's no. of a divisor.

euler's no. can be practically taken as cyclicity in remainders by a divisor..

to find euler's no, express the divisor in terms of prime factors...

100 = 2^2 x 5^2.

powers of the prime nos. have no significance...its jus the prime no. that matters...

euler's no (e for convenience) = divisor x (1-1/first prime factor) x (1-1/second prime factor) x ... (1-1/last prime factor)

so, for 100, e = 100 x (1-1/2) x (1-1/5) = 100 x 1/2 x 4/5

= 40.

that means e for 100 = 40. or, in other words, 100 divisor will definetly show a cylicity of 40 in the remainders.

whenever the power of a relatively prime no. will be a multiple of 40, the expression wud show a remainder 1 with 100.

e.g. 3^120 % 100 = ?

we know e for 100 = 40.
3 n 100 are relatively prime nos.
hence, 3^40 % 100 = 1.

hence 3^120 % 100 = (3^40)^3 % 100 = 1^3 = 1.



7^100 % 45 = ?

45 = 3x3x5

e for 45 = 45 x (1-1/3) x (1-1/5) = 24


hence, 7^24 % 45 = 1

hence, 7^100 % 45 = 1^4 x 7^4 % 45

= 2401 % 45

= 16, the required answer...

Finding remainders using cyclicicty with remainders:

This approach is useful when the divisor is small or at times when it is a factor of 100.

3^327%7 = ?

3^1 % 7 = 3
3^2 % 7 = 2
3^3 % 7 = 6
3^4 % 7 = 4
3^5 % 7 = 4x3 % 7 = 5
3^6 % 7 = 5 x 3 % 7 = 1
3^7 % 7 = 1 x 3 % 7 = 3

remainder 
with first power is same as remainder with 7th power...hence v can say that cyclicity in remainders is 7-1 = 6.

so, 327 % 6 = 3, 

hence, effectively, the remainder is 3^3 % 7 = 6

For Example:
3003^9000%(9*1000)

3003^9000%9 = 0 -----> 9k1

3003^9000%125*8
3^9000%125 = 0 ----> 125a
3^9000%8 = 0 -------> 8b -----------> 1000k2

1000k2 = 9k1 ---> 9000%9000 = 0 
so rem = 0

Tuesday, August 23, 2011

CAT : THE NEW PATTERN


                                                  
                                           SOME OBSERVATIONS


With the new format of CAT launched by IIM’s this past month, students have been forced to alter the way they attempt a paper. In this article I will try highlighting the major changes that the aspirants will have to undergo.

SECTION-1 QA/DI             :                
1)      With 30 questions in 70 minutes, this calculation heavy section will apart from posing problems to those who are weak in Quant; will also trouble people who used to allot greater time to this section from the time left after solving VA in the previous format.
2)      It is not easy to attempt all the questions in QA/DI as it has been found talking to aspirants that they are facing a paucity of time in this section while giving the mocks.
3)      Also, the most important question that arises as how to divide the time among QA and DI.
There is no clarity that QA will feature 20 questions or will QA always be followed by DI?

So, seeing a question and solving it as it comes may not be the best strategy , for you may never know that a easy DI set awaits you after a difficult QA section.
4)       The best way to solve this quagmire is to resort to all sorts of permutations during the mock season. Try different strategies and see which one is working(in terms of time and accuracy)


SECTION-2 VA/LR
1)      Contrary to the earlier section, it is seen that time is being left after solving this section by most people.
2)      Aspirants are submitting the tests before the actual time due to the vast resources available to them (Read:Time).
3)      The most important factor that needs to be then seen is the accuracy .Accuracy could be the deciding factor between a good and a great percentile.
4)      One also should be privy to different types of questions that can be asked in this section:
Critical Reasoning may make an appearance , so also could questions where parajumbles, sentence correction and Fill in the blanks are juxtaposed into 3-4 question sets.


This is the initial view/opinion of most people and it remains to be seen what the actual CAT would look like.




Thursday, August 11, 2011

TO FIND SQUARE OF A 3 DIGIT NUMBER



LET THE NUMBER WHOSE SQUARE IS TO BE CALCULATED BE XYZ.

Sq(XYZ) is calculated like this

STEP 1. Last digit = last digit of SQ (Z)
STEP 2. Second Last Digit = 2*Y*Z +  carryover from STEP 1.
STEP 3. Third Last Digit 2*X*Z+ Sq(Y) +  carryover from STEP 2.
STEP 4. Fourth last digit is 2*X*Y +  carryover from STEP 3.
STEP 5. In the beginning of result will be Sq(X) + any carryover from Step 4.

EXAMPLE:

SQ (421)

STEP 1. Last digit = last digit of SQ (1) =1
STEP 2. Second Last Digit = 2*2*1 + any carryover from STEP 1= 4
STEP 3. Third Last Digit 2*4*1+ Square (2) + any carryover from STEP 2.= 2*4*1 +4= 12
  so 2 would be the third last digit  and 1 carryover
STEP 4. Fourth last digit is 2*4*2 + any carryover (which is 1)  = 16+1=17.
 So 7 and carry over 1.
STEP 5. In the beginning of result will be Sq (4) + any carryover from Step 4.
 So 16+1 =17.

So the result will be  177241.



Hope you enjoyed the concept.