Online CAT Preparation: October 2010

Thursday, October 28, 2010

Palindromes – Interesting Numbers

Posted: 28 Oct 2010 05:23 AM PDT

Palindromes are very special kind of numbers. Typically a palindrome can be described as a number, word, sentence, etc. which reads same forward and backward. Specifically with regards to numbers, Palindromes are numbers which are symmetrical, i.e. they remain the same even when their digits are reversed. For example 14641 is a Palindrome. In fact all the single digit numbers and numbers with same digit repeated are palindromes. So all numbers like 1,2,3…8,9,11,22,99,111,etc. are palindromes.

Features of Palindrome Numbers

1) Reverse a non-palindromic number and add it to the original number. We will get a palindromic number by repeating this process. We may even get a palindromic number in first go. For example, let the original number be 37 (non-palindromic). Add reverse of it 73 to 37, we get 110 (not a palindromic number). Therefore repeat the process. 110 + 011 = 121 (palindromic number). Another example, 16+61 = 77 (palindromic number).

Any number that never becomes palindromic in this way is known as Lychrel Number.

2) A palindromic number in one base may or may not be palindromic in any other base. For example, 1991 is palindromic in both decimal and hexadecimal (7C7)

3) Certain powers of palindromes made up of digit 1,2 and at times 3 are mostly palindromes. For example,

11^2 = 121

22^2 = 484

101*101=10201
111*111=12321 121*121=14641
202*202=40804
212*212=44944

There are, however, an infinite number of cases as demonstrated here:

11^2 = 121, 101^2 = 10201, 1001^2 = 1002001, 10001^2 = 100020001, etc.

22^2 = 484, 202^2 = 40804, 2002^2 = 4008004, 20002^2 = 400080004, etc.

4) All even digit palindromes are divisible by 11. There are many prime palindrome numbers also like 101, 131, 151, 181, and 191

Based on the above knowledge take this very interesting palindrome challenge -

1) Give an example of known "Lychrel Number"

2) Give me the most recent palindromic date.

3) Most of us have lived through two palindrome years, 1991 being the last one. Only 11 years separate 1991 and 2002. Most palindrome years are separated by 110 years. Has there ever been a time when two palindrome years have been separated by less than 11 years? (Here I am not talking about single digit palindromes)

There are many other interesting features related to palindromes. Share with us if you know about it. Post a comment below to share with everyone.

Monday, October 25, 2010

Climbing Problem of Creepers

Posted: 25 Oct 2010 02:14 AM PDT

Another puzzle for you guys. I know there are lot of puzzle enthusiasts out there.

This is an interesting puzzle related to understanding of circular motion. You can solve the puzzle by logic or having some basic mathematical understanding of circular motion. Try it out!

Puzzle

Two creepers, one jasmine and the other rose, are both climbing up and round a cylindrical tree trunk. The jasmine twists clockwise and the rose anti-clockwise, and they both start at the same point on the ground. Before they reach the first branch on the tree the jasmine has made 5 complete twists and the rose 3 twists.

Not counting the bottom and the top, how many times do they cross?

Data Interpretation Questions With Answers

Posted: 24 Oct 2010 07:50 AM PDT

Data Interpretation Questions With Answers: Direction for next 4 Data Interpretation Questions: Answer the data interpretation questions based on the following information:

The year is 2089. Beijing, London, New York and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC.

In any round of voting the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event.

A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible cast a vote in a given round if vote the city (s) he votes for in earlier rounds are out of contention in that round of voting).

A member is also ineligible to cast a vote, in round if the city (s) he represents is in contention in that round of voting.

As long as the member is eligible, (s) he must vote and vote for only one candidate city in any round of voting.

The following incomplete table shows the information on cities that received the maximum and minimum votes in different, the number of votes cast in their favor and the total votes that were cast in those rounds.

Round	Total Votes cast	Maximum votes cast		Eliminated
Round	Total Votes cast	City	No. of votes	City	No. of votes
1		London	30	New York	12
2	83	Paris	32	Beijing	21
3	75

It is also known that

All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.

Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.
The difference in votes cast for the two contending cities in the last round was 1.
50% of those who voted for Beijing in round 1, voted for Paris in round 3.

1. What is the number of votes cast for Paris in round 1?
a. 16
b. 18
c. 22
d. 24

2. What percentage of members from among those who voted for Beijing in round 2 and were eligible in vote in round 3, voted for London?
a. 33.33
b. 38.10
c. 50
d. 66.67

3. Which of the following statements must be true?
A. IOC member from New York must have voted from Paris in round 2.
B. IOC member from Beijing voted for London in round 3.
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B

4. What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?
a. 33.33
b. 50
c. 66.67
d. 75

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Something for the Chickens

Posted: 22 Oct 2010 05:23 PM PDT

A simple mathematical logic says -

odd + odd = even

odd + even = odd

even + odd = odd

even + even = even

Now since you know this have a look at the small riddle below -

A friend of mine runs a small poultry farm in Bangalore. She took me round to see the place. I counted the number of chickens. There were 27 of them. And there were 4 enclosures. I noticed that in each enclosure there were an odd number of chickens.

Can you tell how many there were in each enclosure?

Wednesday, October 20, 2010

Divisibility Rules for 7 , 11 and 13

Posted: 19 Oct 2010 11:58 PM PDT

A guest post by Cecily Zacharias from Oklahoma city, The United Sates of America

Rules for divisibility of 7 , 11 and 13

It is equally good for 11 and 13.

Step 1 Divide into groups of three from the right. 245782 245 782

______________________________________________________________-1 1
Step 2. Write 1,-1,1,-1(alternate 1 and -1) in a row above the number 245 782
( start at the right end and go left)

____________________________________________________________-1            1
Step 3.   Divide each Group by 7 (or 11 or 13, whatever the divisor is )     245         782
0            5

* You can avoid step 2, by simply subtracting first remainder from the second. In this case it will be simply, 5 – 0 = 5
Step 4. Multiply the corresponding numbers in the top row and bottom row and add 0x -1 + 5x 1 = 5

** Step 4 can also be avoided.
Step 5. a. If the sum obtained is zero, The number is divisible by 7 (or 11 or 13 )
b. If the sum is positive, then that is the remainder when we divide the number by 7 ( or 11 or 13 )
c. If the sum is negative, then add 7 (or 11 or 13 ) to get the remainder.
The sum is always less than the divisor.

In the example given, the sum is 5 . Which can be verified.
When 245782 is divided by 7 by long division, the quotient is 35111 and remainder is 5.

If we test for divisor 11, the bottom row will be 3 1
The sum of products of the two rows is -2. since it is negative , add 11 .
So the remainder will be 9
Actual division gives the quotient to be 22343 and remainder 9.

It is the same method for dividing by 13 too.

If you want you can simplify the steps 2 ,to 4 as
Find the remainders in each group and alternately add and subtract the remainders starting from the right. Then use step 5.

On behalf of all the QuickerMaths.com users, I am highly grateful for her contribution.

Sunday, October 17, 2010

CAT Verbal Ability Questions

Posted: 16 Oct 2010 11:01 PM PDT

Direction for next 3 CAT Verbal Ability Questions: Each verbal ability questions consists of 4 sentences on a topic. Some of them are grammatically incorrect/ inappropriate. Select the one which indicates the correct option.

1.
A. Most mobile phone and cable companies are no longer content just to selling Web access to consumers.
B. After investing in high speed pipes, they also want to peddle more of lucrative products, such as TV programs, movies and phone calls.
C. But selling those extras puts the phone and cable companies in competition with Web services big and small.
D. The network operators could block consumers from popular sites such as Google, in favour of their own.
a) C & D
b) D
c) B
d) A & C
e) C

2. A. A Google- Sun Alliance, if it flowers, could take advantage of new technology for running applications on the web, one that eliminates the sluggishness and limited functions of traditional Web-based programs.
B. But advances in technology and the hints dropped by the very secretive Google suggests that it could become a reality few years down the road.
C. In the longer run, however, this could be a big deal indeed for the computer users, especially in home, in school and in small businesses.
D. While lacking some of the polishes of Microsoft Word or Excel, Star Office is more than adequate for most consumers, educational and small business uses.
a) B & C
b) B,C & D
c) A & D
d) A
e) A & B

3. A. Each new Chinese Corporate takeover bid for a multinational company or revelation of a major outsourcing deal elicit howls of protest by U.S politicians.
B. Given their young population, high savings and sheer amount of catching up they still have to do, most economies figure China and India possess the fundamentals to keep growing in 7% to 8% range for decades.
C. Rarely has the economic ascent of two still relatively poor nations been watched with such a mixture of awe, opportunism and trepidation.
D. Studies show the attitudes and aspirations of today's young Chinese and Indians resemble those of Americans a few decades ago.
a) A & C
b) B
c) C & D
d) B,C & D
e) None of these.

Improve your Vocabulary by Free SMS Service

Posted: 14 Oct 2010 09:05 PM PDT

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This is in continuation to the effort of collaborative learning under QuickerMaths.com introduced in the last post - You can make a Difference

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1) English words with their meanings daily. How is it beneficial?

4-5 Words daily. That means : 5x30= 150 words per month and 150x12=1800 words an year. (approx.)
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For any other queries and problems, feel free to mail me at vineetpatawari@gmail.com or info@fireup.co.in

Tuesday, October 12, 2010

Honing a unique strategy to bell the CAT

Posted: 11 Oct 2010 08:28 PM PDT

With just 2 weeks left for CAT 2010 to begin, it is time for you to remain calm and composed. Hitting the panic button, as the d-day is nearing, might be an easier way out but surely not the wisest!

If you already have a strategy in place that suits your individual style, then you are obviously better equipped that the majority but stay grounded. In any circumstance, do not be over-confident.

If you have not carved out a suitable strategy for yourself as yet, NOW would be the time to do it before it is too late. However do not feel disgusted. Remain confident. CAT is not something to be scared of. All you need to do is maintain a balance between speed and accuracy and of course, keep in mind that working smart is more important than working hard!!

Time management is really important at this juncture, both in your daily routine as well as in your test-taking style. Work out a daily routine for yourself giving relaxation its due importance. Keep aside some time for entertainment, exercise and meditation and adequate hours for sleep. Do not set out a very difficult layout as you will not be able to follow it for more than 2-3 days. Set a realistic and achievable target for yourself and stick to this as far as possible.

As far as your test taking style is concerned, do not waste too much time on a particular question. Learn to get over that urge to get the answer if you have already wasted time on it without any results. Solving a question should not become an ego issue. Focus more on accuracy than attempting more number of questions. Believe me, it pays off. Make sure that whatever option you have marked is the right one. It is absolutely fine if you take a few seconds per question extra.

You can make a difference

Posted: 11 Oct 2010 07:17 AM PDT

I remember back to early 2005 (before going for my post graduation), when I'd just started preparing for some competitive examination, that even though I had great ambitions, my knowledge, expertise, and confidence as a student was sorely lacking. My love for internet (as a source of information) made me stumble through various places on the web to know maths short cuts and quick maths tricks, but without much to gain from it.

Now, after having being there and facing it all as a student first and then as a facilitator (though I take good number of Quants classes for CAT aspirants, I would not liked to be called a tutor or a teacher. These titles should be reserved for people of great wisdom and learning) for over 4-5 years I felt I had a really good grip on things; and even then, there were many things I am still struggling with.

Now with the help of QuickerMaths.com, I want to create a platform, easily accessible to the student fraternity where they can get what they are looking for; at least things related to Quantitative Aptitude, Logical Reasoning, Analytical Reasoning and Critical Reasoning - a platform where you can ask questions and where you can give answers.

Let The Process Begin

I'm starting the process by posting below an interesting formula of the topic- time and work . The aim is to initiate the process of collaborative learning. So anyone who wants to make a difference can post a comment with any explanation, formula, shortcut, trick, solved examples, etc. on the same topic (Time and Work for this post). You can also help by sharing the information of this platform with your friends or anyone who wants to help others and learn from others in the process.

You can stay in touch with what QuickerMaths.com is up to through our email subscription method. Also feel free to connect with me on Twitter, Facebook and LinkedIn.

Time and Work Formula

I think the single most useful formula for the topic work and Time ?

N₁H₁D₁E₁W₂= N₂H₂D₂E₂W₁

Where:

N₁ and N₂ = number of person

H₁ and H₂ = Hours worked by per person per day (assumed constant)

D₁ and D₂ = days

E₁ and E₂ = Efficiency

W₁ and W₂= Amount of work done

Consider this example to understand the applicability of this formula –

A piece of work can be done by 16 men in 8 days working 12 hours a day.How many men are needed to complete another work, which is three times the first one,in 24 days working 8 hours a day. The efficiency of the second group is half that of the first group?

Solution –

N₁H₁D₁E₁W₂= N₂H₂D₂E₂W₁

16*12*8*1*3 = N₂*8*24*0.5*1

N₂ = (16*12*8*1*3)/ (8*24*0.5*1) = 48

So number of men required is 48.

Note – you can remove anything from formula is not given in the question. For example if the question would have been –

"A piece of work can be done by 16 men in 8 days working 12 hours a day.How many men are needed to complete another work, which is three times the first one,in 24 days working 8 hours a day."

The applicable formula would have been –

N₁H₁D₁W₂= N₂H₂D₂W₁

Since nothing is mentioned about efficiency, we remove it from both sides.

Thursday, October 7, 2010

Suggested Books for CAT

Posted: 07 Oct 2010 01:08 AM PDT

Lot of QuickerMaths.com users are preparing for CAT and other MBA entrance examinations. In this post I am listing down three most famous books for CAT. First two books are for complete CAT preparation and the last one is for quantitative apptitude for CAT.

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Pearson Complete Guide To The CAT

Author: Nishit Sinha

Nishit Sinha's motto—'Doing the right things and then doing the things right'—is the sure-shot way to success, and is the philosophy behind this book. Providing the student with a detailed inside view to cross the CAT hurdle, Sinha's attention to the each section of the CAT and his tips based on his comprehensive study will go a long way in helping students to succeed in the exam.

CAT Test Suite

Learn and implement new strategies, identify your strong and weak areas, receive personalized feedback and compare your performance to that of your peers. Use the CAT Test Suite on the CD-ROM to familiarize yourself with the online CAT.

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The complete CAT Digest

Author: Arun Sharma

The most famous author of CAT books, Arun Sharma did his PGDM from IIM Bangalore after completing BE in Mechanical Engineering. He has been giving coaching classes for CAT aspirants since 1996. Many of his students have qualified in the CAT and other top MBA entrance tests. Besides, he holds the unique distinction of clearing the CAT successfully 11 times in a row, with a score of 99.99 percentile in CAT 2008.

About the Book

The Complete Cat (Common Admission Test) DIGEST is a comprehensive book that aims to provide the reader with the entire spectrum of the structure, pattern, study methodology, techniques and tips for aspirants to complete successfully in the prestigious CAT examination. The Digest is a one-stop resource for aspirants of this highly competitive exam.

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Other Popular Books by Arun Sharma

How To Prepare For Quantitative Aptitude For CAT

The revised and updated edition of this popular and widely read book for cat aspirants is now in an all-new format and structure. The entire content has been clearly compartmentalized into 7 blocks for a much effective preparation. Based on the latest trends and format of the cat, three levels of difficulty in every chapter, Use of short cuts and techniques both in theory and problem solving processes, Concise organize of the chapters into multiple blocks, varied range of problems with different levels of difficulty.

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Addition of four previous year CAT question papers
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Start preparing from your home by ordering the necessary books for MBA entrance or any other competitive examination from India's best book selling website FlipKart.com

Thursday, October 28, 2010

Monday, October 25, 2010

Puzzle

Saturday, October 23, 2010

Wednesday, October 20, 2010

Rules for divisibility of 7 , 11 and 13

Sunday, October 17, 2010

Thursday, October 14, 2010

Tuesday, October 12, 2010

Monday, October 11, 2010

Let The Process Begin

Time and Work Formula

Thursday, October 7, 2010

Pearson Complete Guide To The CAT

The complete CAT Digest

How To Prepare For Quantitative Aptitude For CAT

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