A Coin Game
Recently, a friend of mine showed me a very interesting game with coins. She asked me to bring three saucers first and she placed them in a line. Then she placed 5 coins of different denominations, one on top of another in the first saucer.
The coins were of the denominations Re 1/-, 50P, 10P, 5P and 25P and she placed the coins in the order of their size—smallest on the top and biggest in the bottom.
She now asked me to transpose these coins to the third saucer observing the conditions that I transpose only one coin at a time, I do not place a bigger on a small one and I use the middle saucer only temporarily observing the first two conditions but that in the end the coins must be in third saucer and in the original order.
‘Oh that’s very simple. This hardly needs much effort’ I said.
I took the 25P coin and put it in the third saucer. Then I kept the 5P coin in the middle saucer. Now I got stuck. I did not know where to put the 10P coin. It was bigger then both!
My friend smiled and said ‘put the 25P coin on top of the 5P coin. Then you can put the 10P coin in the third saucer’.
Memory Tricks for Trigonometry
In the post titled Trigonometry Formula Memorization Trick, I agreed to write about a simple memory trick for memorizing the value of all major angles of different trigonometry ratios like sin30, cos45, tan60, etc. So here you go –
Values of Trigonometric Angles
Let’s start with most commonly used angles of Sin. The angles are 0°, 30° (π/6), 45° (π/4), 60° (π/3), 90° (π/2). For these angles we’ve to make fractions for which we’ve to write 0, 1, 2, 3 and 4 in the numerators and write 4 in the denominator of each fraction.
Quickly Multiply by 21
Rule for multiplying any number by 21
Start from left. Double the first digit and add it to left side neighboring digit. Repeat the steps for subsequent digits. The last number will be same as the last number of the multiplied number.
This rule is very much like the shortcut for multiplying by 11. Since 21 is sum of 11 and 10, it does belong to the same family of short cuts.
Let’s understand the whole concept with an example. Let’s multiply 5392 by 21.
The first digit of the answer will be equal to twice the first digit of 5392. To make the rule consistent assume there is a zero before the number.
Mathematical Symbols Puzzles
We all come across many mathematical or numerical puzzles, which are based on the usage of mathematical symbols or notations. At times such puzzles can even be solved by changing the way things are written.
In this post I am presenting 3 such interesting puzzles. Keen observation and simple application of logic is required to solve them. So here you go -
- Make this equation valid with single stroke of pen (i.e. just by adding a line somewhere): 5+5+5 = 550
- Make 120 using 5 zeros. You can use any mathematical notation/symbol
- What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller
Leave your answers as comment under this post.
Trigonometry Formula Memorization Trick
I learned this shortcut memory trick from my Maths teacher in school. Recently while interacting with a class X student, I realized they have to mug up all the trigonometric ratios. This can be frustrating and can create a phobia or dislike for an interesting subject like Trigonometry at the very onset.
To use this memory trick, you need to memorize this simple mnemonic -
Some people have curly brown hair turned permanently black
That’s all you need to memorize to register the trigonometrical ratios in your mind forever. So here you go,
Shortcut for Addition of Consecutive Numbers
In this post I’ll share with you a useful shortcut maths trick for “finding out the sum of consecutive numbers”. For example, this trick I am talking about can help you in finding the sum of all the numbers from 23 to 31 or any other set of numbers.
Shortcut Addition Trick
Add the smallest number to the largest number of the given set of consecutive numbers. Then multiply the result by the number of numbers in the set. Finally divide the result by two.
Solving the above example, let’s find: 23+24+25+26+27+28+29+30+31
Star Puzzle
Here is an interesting challenge for you. The below mentioned puzzle may appear simple at first, but the solution may be little complex.
Programmers can do some coding to get the answer. If you do that, post it as a comment below. You can use 'trial and error' or any other method to get the answer. So here you go...
Sum on Each Line should be 26
A six-pointed star is drawn with six lines and twelve vertices. Arrange the integers 1 through 12, one on each vertex, so that the four integers on each line add to 26.
Logical Reasoning Books
Reasoning, both mathematical and analytical, probes deep into your logical mind and your ability to comprehend and synthesize the given information. Evaluating various possibilities out of the given information is also essential to derive necessary conclusions.
Here I am trying to compile a list of some of the best books related to logical thinking, data interpretation, data sufficiency and analytical reasoning. What distinguishes these books from the rest is their easy-to-understand format and simple approach to complex problems. I feel that the following logical reasoning books will be really helpful for students who are preparing for Competitive Examinations like LSAT, CAT, GMAT, GRE or any other.
Feel free to suggest any book which you want to be included in this list. I am also putting a link for each book, so that you can order them online and get free home delivery and good discounts. Each book is an investment for lifetime.
List of Best Logical Reasoning Books
I think each book in this list is written in very lucid language and is superb source of knowledge. These books can surely change your conventional approach to reasoning problems.
Click on the “Buy Online” link to read summary and reviews of any book in this list –
1. How to Prepare For Data Interpretation and Logical Reasoning for the Cat by Arun Sharma - Buy Online
2. Pearson Guide to Logical Reasoning & Data Interpretation for The Cat by Nishit K Sinha – Buy Online
3. A Modern Approach to Logical Reasoning by R. S. Aggarwal – Buy Online
4. Logical Reasoning: Test Preparation Study Guide, Questions & Answers by National Learning Corporation – Buy Online
5. Management Entrance Analytical & Logical Reasoning by BS Sijwali, Ajay Singh – Buy Online
6. LSAT Logical Reasoning Bible: A Comprehensive System for Attacking The Logical Reasoning Section Of The LSAT by David M. Killoran – Buy Online
Taking the Headache Out of Word Problems
This is a guest post by Danielle
For many math students, word problems are a cause for anxiety and stress. After all, how can you solve a math problem that is written in words, with few numbers to rely on? In my college trigonometry class, I was guilty of this, feeling like an imbecile as I struggled over the most basic of problems. However, what many don’t realize is that all of the numbers you need are contained in the puzzle; you simply have to know how to recognize and implement those numbers in order to find your solution.
The best way to do this is to draw a sketch of the scenario laid out in the puzzle—in essence to illustrate the story being told—in order to solve the problem. Below are three story problems and a step-by-step guide for finding their solutions:
Trick to Find Square of Numbers from 51 to 59
I’ll share with you one simple method of finding the square of numbers between 50 and 60. Like many other Vedic Mathematics methods, in this method also, we will get the answer in two parts. Since the numbers are in 50s and square of 50 is 2500, we will just use 25 in our calculations, ignoring the zeros.
- To get the first part of the answer, add the digit at the units place to 25 and write the sum
- To get the second part, calculate the square of units place digit and write it
It’ll be easier to understand this with an example.
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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Recent Comments
akbar said that one should get the ring back without climbing into the well. so,birbal... – 18May12
Really thanks .... hats of you ... please tell me such a important tricks of... – 18May12
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