Ramlal is a night watchman in a large company. On one fine morning when Ramlal was about to leave for home, his boss informs him, “I'll go for a business trip to Colombo. Tomorrow I will depart from Chennai airport”.

Ramlal, however advises him to take a ship.

“Why should I?” inquired the boss.

“Yesterday night I dreamt that the plane to Colombo crashes, just before it will land”, is the response from Ramlal.

The president smiles first, but since he is pretty superstitious he decides to take the ship. When he arrives in Colombo, he is told that the plane which he should have taken had crashed. When the president returns from the trip, he gives a big reward to Ramlal and immediately fires him. Why?

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Manorama Yearbook 2012 (Free CD) – This best seller has a long history of success. It is India's best General knowledge update covering almost everything that a student needs in competitive examinations – Purchase Online

General Awareness and Current Affairs Digest 2012 by Krishna Reddy, M Laxmikanth is a Tata Mcgraw Hill publication. This is a comprehensive book full with information and latest data useful for various competitive examinations in segments like civil services, banking, insurance, railways, SSC, Indian Forest Service, NDA/NA, CDs etc. – Purchase Online

Competition Success Review: Year Book 2012 (Wall Maps India & World Inside) by P. N. Kapil can also be very useful for people preparing for competitive examinations like Bank PO, Bank Clerical and Railways and so on.  – Purchase Online

The Pearson General Knowledge Manual 2012 by Edgar Thorpe, Showick Thorpe– Another awesome compilation of the most useful current affairs and general awareness topics and Q&A for competitive examinations. – Purchase Online

The Pearson Concise General Knowledge Manual 2012 by Edgar Thorpe, Showick Thorpe – This is the concise   form of the above book. Overall, this is a good book for Government competitive examinations Purchase Online

The links above are affiliate links to Flipkart. I would request you to read the reviews and take opinion of friends and teachers before ordering any book. I shall be glad to add books suggested by you, to the above list. Please feel free to add your suggestions by posting a comment below.

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Carrying over is a concept taught to us at a very early stage of our life. However, it has never been an easy thing to do. In adding two or more numbers, most of us face problem while “carrying over”. Larger the digits, involved in the numbers to be added, more likely it is to involve carrying.   More the carrying over involved, more likely are we to make mistakes.

Friends, remember the most basic and effective rule of making arithmetic fast and quick is to break difficult calculations into simpler, easily manageable small calculations.

Any digit when added to 9 (except 0) makes carrying over mandatory.  On the contrary, anything added to 0 can’t produce a two digit number.  Even if 9 is added to 0, no carrying is needed.

So, to make things simpler let us create some zeroes.

Example:

Add 38 + 86

First make 38 to 40 by adding 2.  Now obviously adding 86 to 40 is definitely easier than adding 86 to 38.

86 + 40 = 80 + 40 + 6 = 126

I am sure you must be concerned about the 2 we added out of nowhere.  Well you must be, but if you can balance out this extra 2 by subtracting 2 from the answer (126), the final answer will be the same.

You can create 0 towards the end of both the numbers to be added.  Try to understand this with an example,

187 + 139

Add 140 (=139+1) to 190 (=187+3)

140 + 190 = 330

Now deduct back ‘1’ and ‘3’ added to the respective numbers. Hence to balance out subtract 1 and 3 from 330 = 330 – 1 – 3 = 326 is the final answer.

The effect of the above trick can be remarkable. Like any other quick calculation tricks, this also requires a lot of practice to master it.

Check out yourself by adding the following numbers -

37 +54 =?

79 + 23 =?

While adding decimals, this can be a very powerful trick. Try these questions -

12.97 + 1.34 = ?

14.95 + 11.60 = ?

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Brain Games for Your Aging Parents

Just like any other part of the body, the brain has to be exercised to stay healthy. Just like strength training can help muscles to stay strong and running can help the heart stay healthy, regular cognitive exercise can help mental function to stay sharp and to stave off memory loss and dementia. Though the effects of age and time cannot be avoided over time, performing mental exercise can help delay those effects and keep the mind healthier for a longer period of time. Here's how brain games can help your aging parents:

Benefits

There are many benefits of brain games and other mental exercises, like learning new skills or hobbies. Here are a few of the benefits:

• Development of new cells
• Increased blood flow (which also brings oxygen) to keep cells healthy
• Slowing of degeneration
• Improved memory
• Improved concentration
• Strengthened communication pathways between cells

Research has shown that these benefits of brain games and other mentally stimulating activities can help delay the effects of aging, such as dementia, memory loss, or slowed mental functioning. However, these exercises cannot prevent this decline or the onset of disease that impairs mental function.

Types of Games

There are many types of games that adults can play to help improve mental functioning. Games that require problem solving, critical thinking, use of memory or logical reasoning are all beneficial. Here are some other ideas for brain games that are beneficial for the elderly:

• Crossword puzzles
• Sudoku
• Chess
• Card games such as Spades or Bridge
• Board games such as Scrabble or Monopoly
• Jigsaw puzzles
• Logic puzzles

Many more games can be found online or in puzzle books. Look for those that present logic puzzles or mathematical challenges. The AARP has a list of brain games (http://www.aarp.org/health/brain-health/brain_games/?CMP=KNC-360I-GOOGLE-HEA-BRH&HBX_PK=brain_games&360cid=SI_213468091_10055950621_1) specifically designed for improving cognitive function in the elderly on their Web site.

Incorporating these games and logic puzzles into a daily routine, just like exercise, can help seniors to sharpen cognitive ability and delay the onset of aging-related mental decline. Other mentally stimulating activities such as learning a new language or socializing with friends can also provide these cognitive benefits. You can help your parents keep their mental functioning sharp by providing some of these games and opportunities, or by encouraging them to try these new activities.

About the author:
Amanda Tradwick is a grant researcher and writer for CollegeGrants.org. She has a Bachelor's degrees from the University of Delaware, and has recently finished research on college student grants and federal nursing grants.

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Life Is A Gamble: Mathematics Of Expected Value And Insurance Explained

It’s always interesting when someone makes the claim that they don’t gamble. Even this early in the year most people will have made several decisions where the outcome was uncertain and those outcomes were mostly financial - just like a bet. Whether it was deciding to start the year with a new job or take out some kit car insurance on the newly built love of their lives they can’t be sure whether their financial position will be stronger or weaker as a result of their decision.

We’ll first explore the simple mathematics behind these gambles using a gambling example and explain why some decisions you should take each and every time they are offered to you. Interestingly products like insurance rely on our fear of ruin and are not always a fair gamble; we’ll explain why that is and how that leads to profit for insurance companies.

Assessing The Expected Value Of A Decision

When faced with a decision which has primarily financial outcomes it is natural that you would want to choose the option which provides the greatest expected financial return. Assessing this is simple and is shown below:

Expected Value = Probability 1 x Value of Outcome 1 + Probability 2 x Value of Outcome 2...

A simple example is a game of dice. The drunken gambler at the local bar offers you the chance to play a game. If the dice rolls a 4, 5 or 6 he will give you 15. If the dice rolls a 1, 2 or 3 you will give him 10.

EV = (0.5 x 15) + (0.5 x -10)
= 2.5

A normal casino game is always designed so the casino will win in the long run. In this game the player is being offered by the drunk gambler a game where the expected win is 2.5 per game by paying more when a 4, 5 or 6 comes despite the chance of them rolling is exactly the same as a 1, 2 or 3. Since this is a positive expected value the player should sit and play all night. We can calculate the expected value of a thousand games simply by multiplying the expected value of one game by one thousand.

EV(1000 Games) = 1000 x 2.5
= 2,500

The Profits Of Insurance

Insurance has sometimes been called a ‘sucker bet’ because it is perceived to have a negative expected value to the buyer of the policy and the likelihood of claiming is relatively low. The combination of these two factors usually makes it extremely profitable for insurance companies. The annual results of the big life insurance firms make this point very nicely!

“I got an online quote from an insurance company in the UK and was given the figure of £10 a month for a 40-year package of £100,000 cover. So (breaks out calculator) I pay the insurance company £4800 over the course of the policy and when (because it's not an if) I die they pay my beneficiary £100,000.”
http://boards.straightdope.com/sdmb/showthread.php?t=473242

This question shows a big part of why insurance looks to be better value to most people than it actually is. In this case by giving the insurance company £10 per month the customer is forgoing the ability to invest that money elsewhere. If investment rates were 0% so all we lost by buying the policy was £4,800 we can calculate the break even (EV=0) chance of death at that policy price as below where Pd is the probability of death.

EV = Pd x £100,000 + probability of surviving x -4800

=> 0 = (Pd x £100,000) - £4800(1 - Pd)

=> 0 = £100,000Pd - 4800 + £4800Pd

=> 4800 = 104800Pd

=> Pd = 4.58%

In reality though we lose the total value we could have received for that money. If the £10 per month had been invested and returned £10,000 at the end of the period then the probability of death to break even is 9.09%. This is important because insurance companies will be investing the money and will know what your probability of death is fairly well based on their actuarial calculations. If the applicants actual probability of death is 7% during that term let’s compare the perceived EV(1) seen from the perspective of the person asking the question with the actual EV(2) based on the value of the money if it had been invested.

EV(1) = 0.07 x 100,000 - 0.93 x 4800
= £7,000

EV(2) = 0.07 x 100,000 - 0.93 x 10000
= -£2300

As you can see our applicant perceives a positive EV situation when in fact the insurer is set to make a nice profit over their thousands of customers by calculating their investment returns and probabilities of death correctly.

Fear Of Ruin

The final factor to consider when understanding why consumers will take these negative EV bets by taking insurance is the insurers attitude to risk and their corresponding fear of ruin. If our applicant owns a nice house with a £100,000 mortgage in the above example and wants to protect their family from losing their home should they die the £10 per month is a very small commitment in the event they survive whereas the £100,000 mortgage is a very large commitment for the surviving family members.

Consumers are prepared to pay (through taking a negative EV bet) for this peace of mind and this allows the insurers to make a larger profit than they could simply through better calculating investment returns and risk of death than consumers are able to - although naturally as we saw in the question earlier this better ability to perceive these factors is a significant part of their profitability.

This is a guest post by Izzy Woods.

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Imagine you are in a big house and you need to match out the 3 switches located in the first floor with the three light bulbs located in the ground floor. In the ground floor there are 3 bulbs (all are off at the moment), each switch belongs to some bulb.

Question

How can you find out, which switch belongs to which bulb?

Other conditions

It is impossible to see from one room to another.

He can only get down only once to check out the bulb.

Only hands are used. No other device.

Leave your answers below as comments.

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This puzzle is a DTI--Debt-to-Income--problem that banks usually utilize to calculate whether or not a potential borrower will be able to pay back the loan.

Background Info: Mr. and Mrs. Abrams have a combined yearly income of $90,000. They would like to purchase a commercial property on which to start a business for $215,000. They have spoken with a potential lender, who indicated they can provide a $200,000, 30 year loan at 7% interest if the Abrams can qualify. In addition to the property payment, the Abrams estimate their taxes and insurance to be $145 per month. Mr. Abrams has a student loan payment of $67 a month and Mrs. Abrams has a car payment of $347 a month. Assume an amortization factor of 6.65.

Question: Will the Abrams be able to qualify for this loan?

Do your own calculations, and then check below for the right steps and the correct answer.

Step One: Calculate their monthly income by dividing $90,000 by twelve. Their monthly income is then $7,500.

Step Two: Calculate their property payment by taking into account the amortization factor for a 30 year long at 7%. Their estimated monthly payment is $200 multiplied by 6.65 amortization factor, leaving them with a $1330 monthly payment.

Step Three: Calculate their total PITI and monthly debt. The $1300 a month, added to the $145 month, means their monthly expenses are $1475 per month. Their total monthly expenses then include the $1475, plus their $67 and $347 payments, bringing them to $1889.

Step Four: Calculate their Debt to Income Ratios. The first ratio is the $1475 expense versus their $7500 income, meaning that they are under the 28% threshold the bank requires. Their full expenses of $1889 versus their $7500 monthly income is just over 25%, which is still well below the 36% the bank requires.

Solution: Their percentage of monthly income to monthly debt is high enough that they do qualify for the loan!

Danielle is a math whiz with a keen interest in real estate, checking on prices of land for sale in her area and calculating the probability of being approved for loans.

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The Pierrot in the illustration is standing in a posture that represents the sign of multiplication. He is indicating the peculiar fact that 15 multiplied by 93 produces exactly the same figures (1,395), differently arranged.

The puzzle is to take any four digits you like (all different) and similarly arrange them so that the number formed on one side of the Pierrot when multiplied by the number on the other side shall produce the same figures. There are very few ways of doing it, and you shall give all the cases possible. Can you find them all?

Remember you are allowed to put two figures on each side of the Pierrot as in the example shown, or to place a single figure on one side and three figures on the other. If we only used three digits instead of four, the only possible ways are these: 3 multiplied by 51 equals 153, and 6 multiplied by 21 equals 126.

Leave your answers below as comments.

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The Great Russian poet Benediktov was very fond of mathematics and he collected and compiled a whole volume of trick brain teasers. Though this work was never published, the manuscript was found in 1924. An interesting problem contained in the manuscript, captioned ‘An ingenious Way of Solving a Tricky Problem’ goes as follows:

One woman made a living by selling eggs, had 90 eggs which she wanted her three daughters to sell. So she gave her eldest daughter 10 eggs, 30 to her second daughter and 50 to the youngest.

'You better agree among yourselves', she told them; ' about the price you're going to ask fo you eggs, and stick to it. But I hope that the eldest will receive as much for her 10 eggs as the second will for her 30 eggs and the third for her 50 eggs. In other words each of you should bring back the same amount of money and keep in mind; the total for 90 eggs should not be less than 90 bucks.

I found this interesting puzzle from the book named More Puzzles by Shakuntala Devi.

Post your answers below as comments or discuss it on the QuickerMaths facebook page.

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The Rule of 72 is a good quick math shortcut to find out the following –

• Time required for an amount to double itself, at a given rate of interest
• Rate at which an amount should grow to double itself in given time

This formula can be applied for “Doubling Problems” related to money, population, etc. which grows at an annual compounded rate.

Formulae

1. To calculate the time; T = 72/R
2. To calculate the rate of interest; R= 72/T

T = Time required to double a sum of money at the rate of R% per annum.

R = Rate of interest at which a sum of money gets doubled in T years.

Explanation of the formula  

To find out the number of years required to double an investment in a fixed deposit which gives you 9% rate of interest compounding annually, divide 72 by 9.

For example, if you invest Rs. 10000 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to become Rs. 20000; an exact calculation gives 8.0432 years. So there is small margin of approximation.

The above formula is more accurate at lower interest rates (say up till 10%). The approximation error starts increasing after that.

In case of continuous compounding, 69 instead of 72, gives more accurate results. However, in our day to day life the concept of continuous compounding is rarely used.

Guide to Online Schools has information on math classes.

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