LAST TWO DIGIT

Dear student, Agenda is how to calculate last two digits of the number ending on 1.
Last digit or unit digit will be always 1.
Just observe tenth place digit in following example
11^2 = 121 (1 * 2 = 2)
11^3= 1331 (1 * 3 = 3)
21^2 = 441 (2 * 2 = 4)
21^3= 9261 (2 * 3 = 6)
Just apply this technique to the following examples
Example: 31^8
If number is ending on 1 last digit is always 1.Important is how to calculate Tenth place digit. It is also very easy. Tenth place digit will be (3 * 8 =24) so tenth place digit is 4
So last two digits of 31^8 is 41.
Find the last two digits of 41^2789
In no time at all you can calculate the answer to be 61 (4 × 9 = 36. Therefore, 6 will be the tens digit and one will be the units digit)
Find the last two digits of 71^56747
Last two digits will be 91 (7 × 7 gives 9 and 1 as units digit)
Now try to get the answer to this question within 10 s:
Find the last two digits of 51^456 × 61^567
The last two digits of 51^456 will be 01 and the last two digits of 61^567 will be 21. Therefore, the last two digits of 514^56 × 61^567 will be the last two digits of 01 × 21 = 21
Last two digits of numbers ending in 3, 7 or 9
Find the last two digits of 19266.
19^266 = (19^2)133. Now, 19^2 ends in 61 (19^2 = 361) therefore, we need to find the last two digits of (61)133.
Once the number is ending in 1 we can straight away get the last two digits with the help of the previous method. The last two digits are 81 (6 × 3 = 18, so the tens digit will be 8 and last digit will be 1)
Find the last two digits of 33^288.
33^288 = (33^4)72. Now 33^4 ends in 21 (33^4 = 33^2 × 33^2 = 1089 × 1089 = xxxxx21) therefore, we need to find the last two digits of 21^72. By the previous method, the last two digits of 21^72 = 41 (tens digit = 2 × 2 = 4, unit digit = 1)
So here’s the rule for finding the last two digits of numbers ending in 3, 7 and 9:
Convert the number till the number gives 1 as the last digit and then find the last two digits according to the previous method.
Now try the method with a number ending in 7:
Find the last two digits of 87^474.
87^474 = 87^472 × 87^2 = (87^4)^118 × 87^2 = (69 × 69)^118 × 69 (The last two digits of 87^2 are 69) = 61^118 × 69 = 81 × 69 = 89
If you understood the method then try your hands on these questions:
Find the last two digits of:

1. 27^496

2. 79^93

3. 583^512

UNJUMBLE YOUR MIND!!!!!!!!!

PARAGRAPH JUMBLES-
Paragraph jumbles of the verbal logic part is almost an inevitable section. The catch lies with the phrase “choose the most logical order of sentences to form a coherent paragraph.” To solve this genre of questions you need to be as mechanical as possible. If you are one of those students who are literally terrified of the Verbal Ability section in CAT, Para jumbles could come to your rescue and bolster your score.
Do you guys remember your childhood days when you used to occupy yourselves with the very interesting jigsaw puzzles; while trying to join the pieces you would put 2 similar looking pieces together, Right? YOU NEED TO DO THE SAME THING WITH WORDS HERE, BY ESTABLISHING A LINK BETWEEN 2 SENTENCES. There would be lot many key words to help you to form the mandatory pair/s e.g.: proper nouns, pronouns: he, she, it, they etc., and conjunctions: although, however, and, also, while, yet, but, besides etc.

For example if there are options like: 1) ABCD (2) ABDC(3) BACD(4) DABC (5)CBAD after reading the sentences ,using the indicator clues you have figured out that AB is a mandatory pair, you can straight go to your options and eliminate ,you will be left with 2 options like in the above mentioned case. Thereafter, you can form bigger sequences, thus deciphering the right answer.
THIS STRATEGY ALWAYS WORKS IN ALMOST ALL CASES.
There are few other strategies as well, which you need to bear in mind while tackling this arena.

1) Identify an obvious beginner (a sentence which introduces an idea) or an obvious conclusion (a consequence or which sums up an idea). Consider this example:

A)He hopes to correct the limitations of cochlear implants through his research.
B)Ruffin knows firsthand; he received an implant 6 years ago.
C)Cochlear implants help bring profoundly deaf individuals into the hearing world, but one HHMI fellow says the technology needs improvement.
D)Chad Ruffin says users have a tough time understanding speech in noisy environments, largely because today’s implants transmit almost no information about pitch.

Here the statement C is an obvious beginner as it introduces the entire topic of cochlear implants. Sometimes an obvious beginner or a conclusion is very evident. This just makes our task simpler.

2) Establish a link and identify mandatory pair/s. In fact identifying mandatory pair/s is a crucial step. For e.g.

A)The service carries a premium: as of mid-1992, several hundreds Washington political insiders paying from $980(for a small firm)to nearly $4500(the white house itself) to read about daily White House activities.
B)Even the most timely industry newsletter is usually at least a week old before it gets to its readers.
C)It reaches paid subscribers 18 minutes after leaving the editor’s desk, by fax.
D)Not the ‘White House Bulletin.’

It’s obvious here that DC is a mandatory pair since the pronoun ‘it’ refers to ‘The White House Bulletin’

3) Something has to be mentioned first and then explained. It’s not very difficult to map the author’s mind, he follows a definite logic, and he would never jump from one idea to another. Consider the following example which I‘ve used to elaborate this point.

A. There is much to be done.
B. Outside in the sunrise garden roses are already awake, clematis climb like a growing child and all the border marigolds are on fire.
C. Climbing painfully from a sore mattress, standing in striped pajamas by the window, Jim stares garden wards.
D. These days it’s all weed killing, backache and wishes.

We need to understand that the garden needs to be mentioned and then described so B will always come after C.

4) Associate keywords and form sequences: Now check this example out.

A. The two neighbours never fought each other.
B. Fights involving three male fiddler crabs have been recorded, but the status of the participants was unknown.
C. They pushed or grappled only with the intruder.
D. We recorded 17 cases in which a resident that was fighting an intruder was joined by an immediate neighbour, an ally.
E. We therefore tracked 268 intruder males until we saw them fighting a resident male.

Here the key words are highlighted. With the help of key words you can understand that BE is related because of the mere presence of the word ‘therefore’ which is an indicator clue and since B has happened it leads to E and D follows from E. This is how you associate keywords and move from smaller sequences to bigger ones.

Try adhering to these strategies and you can crack paragraph jumbles fairly easily.

Analytical Reasoning

There are 5 houses in 5 different colors in a row. In each house lives a person with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage. Other facts
:1. The Brit lives in the red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the immediate left of the white house.
5. The green house's owner drinks coffee.
6. The owner who smokes Pall Mall rears birds.
7. The owner of the yellow house smokes Dunhill.
8. The owner living in the center house drinks milk.
9. The Norwegian lives in the first house.
10. The owner who smokes Blends lives next to the one who keeps cats.
11. The owner who keeps the horse lives next to the one who smokes Dunhill.
12. The owner who smokes Blue masters drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The owner who smokes Blends lives next to the one who drinks water.
The question is: WHO OWNS THE FISH?

I think many of us are aware of divisibility rules but the question is..." why this method?".So let us find out the answer.
1) let's take a three digit no.(rule for 3)
abc=100a+10b+c
= 99a+a+9b+b+c
=(99a+9b)+(a+b+c)
=9(11a+b)+(a+b+c)

now can we say that one part of number is a multiple of 9 and if it is then, number will also be divisible by 3,so we are checking the sum of the digits, which if becomes a multiple of 3 then the complete number also becomes a multiple of 3.


2)lets take a four digit no.(rule for 11)
abcd=1000a+100b+10c+d
=1001a-a+99b+b+11c-c+d
=(1001a+99b+11c)+(b+d)-(a+c)
=11(91a+9b+c)+(b+d)-(a+c)

now can we say that one part of a number is a multiple of 11,so we are checking the difference between the sum of the even and odd places ,if difference comes out to be the multiple of 11 then the entire number is divisible by 11.

3)let us check the divisibility of 7 and 13.(method is same for both 7 and 13).
Take an eight digit number as abcdefgh,now make the sets of three from right to left and then take the difference between the sum of the alternate sets,if the set is not complete put zero before the number.If difference is zero or multiple of 7 or 13 then the number is divisible by 7/13
(fgh+0ab)-(cde)=0 or multiple of 7 or of 13.

CONCLUSION:Any six digit no like(111111,222222,333333........)is always divisible by
7/11/13.For 11 also you can use the same method.


Now the question for you that why we make the sets of three in case of 7/11/13.
post your answers and have a coffee with me.

CAT 2008 NOTIFICATION

Important Dates
Issue of CAT Bulletins by Axis Bank STARTS : JULY 14, 2008 (Monday)
Issue of CAT Bulletins by Axis Bank ENDS : AUGUST 8, 2008 (Friday)
Issue of CAT Bulletins by IIMs ENDS : AUGUST 13, 2008 (Wednesday)
Last date for receipt of completed CAT Applications by the IIMs : SEPTEMBER 5, 2008 (Friday)
COMMON ADMISSION TEST : NOVEMBER 16, 2008 (Sunday)

CAT forms are available at following Branches of Axis Bank in Pune:

1. JM Road.
2. Kothrud.
3. Camp.
4. Pimpri Chinchwad.
5. Sahakar Nagar.

Para Completion Deciphered

Well I am back after a considerably long hiatus.This time I am going to give you all some dope on the Verbal Logic section.This is for all the CAT-08 aspirants who have been burning themselves out on questions from Para completion.This section has been quite ubiquitous in CAT for the past two years and is very probable in 2008 as well.The biggest challenge,that the takers face here is the ambiguity of the options.The point to be kept under consideration is that,the question will generally require you to "Choose the best possible answer" which insinuates that there exists a possibility of more than one correct answer.Now what to do?Again in a conundrum!There is no need to fret!Remember there are certain yardsticks that one can use as a checklist to strike-off the options that do not seem to fit in perfectly.For example,one or two options can be clearly negated on account of being"Out of Scope",i.e. not being in direct relation to the context.Same rule applies to an option that seems to regurgitate the same idea mentioned in the passage(That would rather qualify as the summary).Remember your correct option will NEVER be a restatement from the paragraph given.Narrow down your choice to the option that not only seems to take forward the main idea of the passage but also has the connotation of a closure(Alomost the same logic that we apply to locate the last statement in parajumbles.
All said and done the best way to crack this section is to practice as many questions as possible to identify the grey areas and I am sure you can start experimenting with the tips mentioned here in your MOCKS to overcome the ambiguity of the VERBAL section!!!!

Best of Luck for ALL-INDIA MOCK CATs starting 13th July,2008!