Best of CAT (Common Admission Test) - 2

This post is the second in the series of my efforts to solve some of the best CAT problems in both theory and programming. It gives me a great pleasure to solve and then verify the answers to some puzzles using C++ or Python and sometimes SAS.

Here is an interesting puzzle that will make you look like a geek (or a nerd - depends on how you look at Mathematics) when you pose it to a group.

Question: There is a certain number X which when divided by Y, where all Y ε [1,10] yields a remainder (Y-1). That is, when X is divided by Y, which takes all values from 1 through 10, the remainder is (Y-1). To be more clear, if X is divided by 10 then the remainder is 9, if X is divided by 9 then the remainder is 8, so on and so forth, if X is divided by 3 then the remainder is 2. The condition should hold good for all numbers from 1 to 10. What is the least number X can take to satisfy this condition? (Hint: X is less than 3000.)

Solution: I programmed this in C++ and it is pretty straight-forward.

The same thing can be implemented in SAS. Let me withhold the answer for now.

Coming to the more important part - to solve this problem by implemting theoritical concepts. This problem pertains to Number Theory. 'Least Common Multiple' doesn't need any introduction. When there are a set of divisors that yield the same remainder (Remainder = 1 in this case), the least number that satisfies this condition =

LCM of those divisors - Common remainder.

By solving, the LCM of numbers 1 through 10 is 2520. Hence the answer = 2520 - 1 = 2519.

All multiples of LCM have the same property. (5040 - 1), (7560 - 1) etc, all have the same property. The objective here is to obtain the least number which satisfies the condition which is 2519. More often than not, confusion prevails in CAT. Also, time is premium in these tests and so the standard method of obtaining LCM may not work well if the divisors are too many or too big. Taking cues from the answers and back solving will be lot helpful. In this problem, it is stated that division by 10 yields 9 which implies that the last digit is 9. That holds the key to solve this problem.

Google's Chrome: What's the strategy?

It is disconcerting to even start thinking that Chrome was launched just to take on Microsoft's Internet Explorer or Mozilla's Firefox. I am pretty sure that this is not high on the 'Mission' list of Google, though a direct competition is intentional and inevitable. That leads to the question - What could be the strategy behind this move. Google is always known for its innovative projects and subtle debuts. They have a vast repertoire of such products and you never know what is coming next. This unpredictablity is Google's greatest weapon. Anyways, moving on to Chrome.

Let me start from the basics. Why do we need a computer? In no particular order - we use computers for casual browsing, news, personal (music/media), chat, office work (technical & non-technical stuff). There could be couple of other things that I may have missed out. Most of these, infact all of them, have been traditionally on desktop software. And this is Microsoft's stronghold. There are some conventions that we got used to - like saving our files on our hard-disks, transferring files using optical media, using the computer to access internet. And then came Google, riding the internet wave.  And it had a web-based business model. In other words, Google wants to use the potential of internet as an application platform and move the market away from conventional PC-based environment to a web-based one. And the starting point for this transition is Chrome. 

One may wonder the necessity to come up with a new browser when big guns IE, Firefox and Safari have saturated browser market. Well, for a complete integration of all its web-based applications it is no-brainer that Google will want to come up with an in-house browser than rely on a 'third-party' browser. It will give them better control on scalability of their applications and control over the evolution of various components related to their business. The beta version of Chrome is adequate. Firefox and IE 8 are far superior in features and reliability to Chrome but it is foolish to compare these three at this point. Chrome is in its infancy and is building a base to lauch its horde of services. Google's core business - its search engine is, ofcourse, web-based. The applications they provide like GMail are on the network. Google docs, a direct competitor to MS Office, is web-based. All of these help Google rake in advertising. So, what's the need for desktop software? Read Windows, Office.

It is too early to predict the penetration of Chrome into the browser market. The features are minimal but the potential is maximal. Once Google is ready to integrate its applications to Chrome, imagine this, all one needs to do is boot the computer and open Chrome. You can search from Chrome's navigation bar, open office suite from Chrome, chat through Chrome, watch movies here and what else do you need to do?

And what could be the impact of Chrome on Microsoft? Microsoft is tied to its legacy model of selling licenses of Windows & Office and is now realizing the potential of internet. Microsoft Office has a lion's share in Microsoft's revenue. And if Google can capitalize on its online office suite, it would be a huge blow to Microsoft. But, it'd be naive to write off Microsoft. Who know what they have in store. Are they transitioning to an online-office model? Not easy but not impossible either. For their benefit, I feel Microsoft should stop worrying about 'fancy vista' stuff and concentrate on functionality and user friendly apps/suites. Else they could find themselves swimming upstream very soon.

So, Chrome is here to stay. It cannot be compared to IE or Firefox right now, but I feel it has the ability to better both these browsers and above all, be more useful to the user. There are many 'to-do' items for Chrome of which the most important are stability and security. It's still a beta so chill and wait for the real version to roll-out.

Lehman Brothers Bankrupt - Why and how it happened.

As a prospective MBA student and one really keen on investment banking - Lehman Brothers is a big name to me. It is the same with many prospective and current MBA students across top B-Schools all over the world - IIMs, ISB, Wharton, Harvard and what not? A glimpse at Wharton's MBA placement statistics for 2007 shows that Lehman recruited 18 grads. It could be around the same number of students placed across other top B-Schools here in USA. And the doomsday came on 15th September. Lehman filed for Chapter 11 Bankruptcy. This is what it posted on its website at midnight of the 14th.

"Lehman Brothers Holdings Inc. Announces It Intends to File Chapter 11 Bankruptcy Petition; No Other Lehman Brothers' U.S. Subsidiaries or Affiliates, Including Its Broker-Dealer and Investment Management Subsidiaries, Are Included in the Filing."

It is indeed a red letter day in USA's corporate history. A 158-year old company has filed for a bankruptcy and wrecked Wall Street and rattled the global finance system. Also rubbing salt to the finance industry's wound, is Merrill Lynch's demise (read as acquisition) by Bank of America. Two majors down on a day. But what actually happened at Lehman? This is my two cents on the issue.

"Know when to stop before you begin" goes the saying. Lehman got this messed up. Investment banking was always about high-stake bets and huge borrowings but it also demands high level of strategy. It is believed that Lehman borrowed too much money and invested it in 'very high' risk domains, namely real estate. Success in IB is proportional to the ability of that company to take risks. But there is thin line that separates risk from imprudence or over-confidence. More so when we speak of real-estate investments in this economy. Clearly Dick Fuld, Lehman's CEO got his priorities and numbers wrong. 

But as the credit crunch worsened, Lehman's leverage - borrowings relative to capital - continued to grow. This is in contrast to other major IBs. One instance of Lehman's miscalculated investment is its leveraged buyout of Archstone, a big apartment developer. Lehman paid $22.2 billion for this transaction (in partnership with Tishman Speyer) in Oct 2007. By then, real estate woes have already begun. But how prudent is that investment? Lehman's shares have lost 94% of their value since the beginning of this year due to its exposure to subprime debt crisis.

And on 15th of September came the bang. The filing shows that Lehman is closing its doors with more than $600 billion of debt. The bank has total debts of $613 billion against total assets of $639 billion. Its filing with the Bankruptcy Court of the Southern District of New York shows that Lehman had more than 100,000 creditors. The move into bankruptcy came after last-minute talks with Barclays PLC  and Bank of America faltered Sunday, leaving few options for the 158-year-old firm.

Many of us know that Lehman is actually a 14 year company with a 158-year name. That is because it was acquired by American Express in 1984 and spun-off in 1994 as a standalone company. Sadly, over the last week or so, Lehman was like a bug dying on your windscreen: you want to focus on the road but are compelled to watch the stricken insect’s last moments.

Good-bye Lehman.

A paradise called Ventura!

What was supposed to be a business trip turned out to be an immensely relieving and refreshing personal trip as well. My conference at in Ventura, CA gave us some wonderful moments to cherish and even better weather to relish. 

There are very few things that I am a captive of. Nature is foremost amongst them. And nature in any form of water – lakes, rivers, seas or oceans, enthralls me the most. My hotel was on the pacific coastline. My room overlooked Pacific Ocean. What more can I ask. I spent hours effortlessly watching the waves splash the coast. Whenever I had a break in my conference, I was back in my balcony watching nature at its best. 

For someone from Phoenix which has an average summer daytime temperature of 110F, 70F on the coastline is a dream come true. Throw in a resort-type atmosphere, a laid back but interesting conference and paid trip into the mix and the outcome is very satisfying. It is not an overstatement that this is the best personal trip I’ve had. I did not attend the casual dinners that were included by my conference sponsor. All the 4 days, I had my dinner out with my wife, after we spent hours on the beach sand. I could see the ocean meeting the sky at the end of horizon on all the three directions and it was a treat to watch.

 Sometimes, I tried preparing for the conference and the presentation that I was supposed to deliver  by sitting on the balcony deck that faces the ocean front and all that I ended up doing was watching the endless magical waves. I strongly recommend Ventura and its surroundings as a very good vacation spot. I see myself visiting Ventura often in the coming days, thanks to US Air.

Federer reigns.

As expected (and as I hoped), Federer won US Open and with that created record of sorts. He is the first player in the history of tennis to win five successive titles at two different grand slam events (Wimbledon & US Open). 6-2 7-5 6-2 showed how stark the difference was between Federer and Murray, a first-time grand slam finalist. Federer started the match with an ace and from then it is history.

There is something I always believe is true about Roger Federer. He is the best tennis player ever. I admired Borg, Sampras, Agassi but none so much as I did Federer. That is because of his versatility. His all-court mastery coupled with extraordinary athleticism and determination puts him way across the rest (excluding Rafael Nadal, who is not very far off). But Nadal has lots to prove and achieve to even be compared with Federer. He has a long way to go and the more tougher part is remain consistent as Federer to be considered as a great player. Federer was stung by mononucleosis which affected the way he played over the last couple of months but it is a great time to come back and prove your fans and detractors wrong. Isn't it?
All said and done, I still do not like Federer winning in straight sets. I like to see someone (Nadal for instance) stretch Federer into 5-sets like in this year's Wimbledon final. And then I like to see Federer win. That extracts the best tennis from Federer. Some of his shots under pressure are a treat to the eye. The angles that his cross-courts create are mind-boggling. That is what I yearn to see from Federer - high quality tennis and not 6-0 6-0 6-0 domination stuff.

A thing of beauty is a joy forever. And so is Federer's tennis.