How To Do Probability - Aptitude for Competitive Exams

Probability, an important area for almost all Competitive Exams. When we started posting Quantitative Aptitude Shortcut Tricks, many people asked us to post some questions about Maths Probability Help. We are keep on postponing this request because we feel simply posting some questions wont help really. So finally here we came up with this shortnotes on Probability which really helps you in getting good marks in Probability and Statistics section of Maths in Bank and all Competitive Exams. In this notes we've started with the basic details like definitions and later explained the concept with problems. We've tried to give detailed explanation for every problem we've mentioned in this small book. Good Day and Happy Reading :)

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R. S. Aggrawal's Quantitative Aptitude - Pdf

Thanks for the response to our previous post, the pdf version of R.S. Aggrawal's Verbal Reasoning. As number of our friends here are asking us to post the pdf version of R. S. Aggrawal's Quantitative Aptitude, so in this post we are updating the pdf version of the Quantitative Aptitude. This will help you preparing for the Aptitude section of Any competitive Exam in India. And friends, plz remember that just saving this file in your system wont help you. Do practice daily. Here is the Download Link (Click on the slow download button and wait). Please Like us at Facebook for frequent updates. You can get more downloads Here. All The best and Happy Reading.

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Speed Maths shortcuts - Pdf version

Friends, we've got tremendous response to our previous pdf post of the shortcuts about Squares, Square roots and Cube roots. First of all thanks for the support. So many of our users have asked to upload the shortcuts for doing basic maths like additions, subtractions, multiplications and divisions etc.   So for you we are posting the shortcut tricks for mental maths. In this post you will get the shortcuts for finding almost all the mathematical problems (including square roots and cube roots). Hope this post will help you in improving your problem solving skills. You can get more downloads here. Please LIKE our facebook page here for frequent updates. Happy Reading :).

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Speed Improvement Test - Day 8

Recommended Time : 15 Mins

First to these tests? Start the tests from Day 1

Percentages

1. 55.55% of 468 = ?
2. 15.88% of 510 = ?
3. 34.09 % of 792 = ?
4. What percentage of 933 is 588 ?
5. By what percentage is 412 more than 322 ?

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Key - Speed Improvement Test - Day 8

Recommended Time : 15 Mins

<< Read Questions Here

Percentages

1. 55.55% of 468 = 260
2. 15.88% of 510 = 80.988
3. 34.09 % of 792 = 270
4. What percentage of 933 is 588 = 63%
5. By what percentage is 412 more than 322 = 27.95%

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Data Interpretation

Data Interpretation,  the one of the easiest, time taking and scoring topic of the Bank Exams.  Everybody knows this fact... but people pay less attention on this area. But unfortunately in SBI PO Exam, the complete aptitude section will depend on Data Interpretation. So you should concentrate more on this area.

In this post, we shall discuss about the basics Data Interpretation.  The Data Interpretation is also called as comprehension of mathematics. Because, in reading comprehension, we have to study the passage and answer the questions followed by that passage. In the same way, in Data Interpretation, some data is given in the form of graphs, charts and tables followed by questions. We have to study, understand and analyze the data to solve the questions. Here we have to keep in mind that, even a 10th standard boy can solve these problems. But you've to solve these problems IN TIME.

So you have to practice well so that you can do the small calculations (like additions, subtractions, and simple multiplications) with a glance (see here for shortcuts in mental maths). Now lets have a look at some basic details of Data Interpretations.

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Time, Distance and Speed

Today we shall discuss another important topic of Aptitude - Time and Distance. In these type of problems you have to do problems on the speed of Train, Boat etc. Initially these problems may look little confusing, but if you practice well these are very interesting, easy to solve and help you to get good marks. But please keep in mind that the problems of this type are little confusing, people often lose marks because of their lack of concentration. They may feel that they've got the correct answer and choose the answer according to that, but they often endup forgetting CONVERSION (you will know what we've meant by this conversion later). Now before going into details, lets discuss some useful formulas of Time, Distance and Speed.

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Shortcut for finding Cubes

Attention Friends... we've came to know that this method is not working for some numbers... So presently we are working on more efficient method than this... We advise you to avoid this method....

In our last posts we've discussed the method of finding Squares (read that post Here). In this post we shall discuss the method of finding cubes. This is very easy and simple method. You just have to put little concentration while learning and should do little practice so that you can do the process in a easy way mentally. And another thing you should keep in mind is, we are posting the step by stem inorder to make you understand the process in detail, but you SHOULD do most of these steps MENTALLY and only should put some important final results on paper. Now lets have a look at the method. In earlier method of finding squares we'd discussed finding the squares with the formula (a+b)², here we shall use the formula (a+b)³. 

Lets start with an example. Assume that you should find out the cube of 18. The general process is multiplying 18 to itself for 2 times (18 x 18 x 18). This process is time consuming and often people end up with the wrong answer caused by confusion and hurry. 

Ok, now lets use our method. here you should use the formula  (a+b)³ = a³ +b³+ 3a²b +3ab². But here you should be little tricky. Have a look.........

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Simple Method for Calculating Shortcut for Square - Part 2

We've already seen how to find the squares of numbers which are one more than those whose squares we already know (eg 25, 30, 35 etc).Read that post Here. Similarly, we can find the squares of numbers which are one less than the numbers whose squares are known already to us. For Example,

292 = 30 - 30th odd number = 900 - 59 = 841

392 = 40 - 40th odd number = 1600 - 79 = 1521

342 = 1225 - 69 = 1156

542 = 3025 - 109 = 2916

742 = 5625 - 149 = 5476

942 = 9025 - 189 = 8836

2142 = 46225 - 429 = 45796

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Shortcut for Square - A Simple Method

We have already discussed a method for finding the squares of the given number (check that method Here). Now we shall discuss another simplest method to calculate square of the given number. First of all one thing you should keep in mind, for you r convinience we've mentioned each and every step in detail. But You should do all these calculations MENTALLY. I mean without using pen or pencil. So practice well to do these problems orally. Now lets go to the topic, Finding the square of a number ending in 5 is very simple. If the last digit of the number is 5, then the last two digits of the square will be 25.What ever is the earlier part of the number multiply it with one more than itself and that will be the first part of the answer. (The second part of the answer will be 25 only).

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Shortcut for Multiplication (Base Number Method Part 2)

We've already discussed about the Shortcut Method (Base Number Method) for doing multiplications. In the earlier post we've discussed doing the multiplication by taking the base as 100 (Click Here to read that). I mean, you can do the multiplication for the numbers nearer to the 100. Then what about the remaining numbers? Well, being the Guide 4 Bank Exams we have solutions for all Banking Problems... So, lets have a look at some more approaches of the Base Number Method so that it will be easier for you to multiply any number with any number :)

Find the product of 117 and 88

117   --->   +17

  88   --->   -12

____         _____

105             -204           Ans : 10296

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Shortcut for Multiplication (Base Number Method)

We've already discussed some short cut tips for Multiplications. You can check that post Here. Now we shall discuss another  Simple and Useful method for Multiplication. In this method we take a base (according to the given numbers) and do the multiplication according to that base. Assume that you have to multiply 97 with 92. The power of 10 to which these two numbers are close is 100. We call this 100 as the base. Now write these two numbers with the difference from the base. 

97 ------>  -3  (because 97 is obtained as 100 - 3)

92 ------> -8 (because 92 is obtained as 100  -8)

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Speed Improvement Test - Day 5

Recommended Time : 15 Mins

<< Read Shortcut Techniques Here

Additions / Subtractions

1. 3972 + 7646 + 8791 + 2763 + 9437 = ?
2. 7149 + 3487 + 2983 + 6731 + 8971 = ?
3. 545 - 32 + 217 + 49 - 117 + 81 =?
4. 642 + 717 - 84 + 343 - 119 + 420 = ?
5. 2636 - 1742 + 8346 + 73 - 514 = ?

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Finding the Square of the given Number

In this post we shall discuss about the Shortcut of finding the Square of the Given Number. This is very easy and Simple method. All the you need to learn this method is little concentration and little patience. Remember friends, To make you understand the process clearly, we are posting the process in Step by Step process. But you have to do all these steps Mentally and you should Only write the Answer on Paper... 

Lets start with an example. Assume that you have to find the Square of the number 38.

So, the general process is 38²  multiplying 38 with itself. But this process take much time and effort. So, instead of calculating 38 X 38, just use the formula a² + 2ab + b²

But here you should apply a little trick. If you apply the above formula as it is... you cant get the answer... Just do as mentioned below.

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Profit, Loss and Discount - II

<< Contd from HERE

Knowing the labelled price and the discount percentage and the percentage profit of the seller, we can get the actual cost price.


The selling price fixed by the seller includes all other necessary expenses like taxes, carting expenses etc. By giving some discount, the seller gets more customers.

Note  : Commission or brokerage is Added when we purchase, Subtracted when we Sell.

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Speed Improvement Test - Day 4

Recommended Time : 15 Mins

<< Read Shortcut Techniques Here

Additions / Subtractions

1. 4321 + 64319 + 54321 + 709126 = ?
2. 5321 + 6741 + 8091 + 4678 + 2132 = ?
3. 432 + 216 + 509 + 723 - 625 - 416 = ?
4. 40965 + 60978 - 31241 - 20986 = ?

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Problems on Percentages

Lets do some problems on Percentages  

<< Read Basics HERE 

A's income is 20% more than that of B while B's income is 20% less than that of C. Whose income is the highest amongst all?

 Sol : Let the income of C be Rs. 100/-

            So, The income of B is Rs. 80/-

            A's income is 20% more than B = (120/100) X 80 = Rs. 96/-

           So, obviously C's income is Highest

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Speed Improvement Test - Day 1

Recommended Time : 15 Mins

<< Read Shortcut Techniques Here

Additions / Subtractions

1. 12345 + 34567 + 78123 + 40249 = ?
2. 51241 + 64172 + 81496 + 34567 = ?
3. 19876 + 64321 + 19283 + 40091 = ?
4. 91274 - 40362 + 54321 - 65409 = ?
5. 10568 + 5432 + 246 - 8432 - 4169 = ?

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Mental Maths (Percentage Calculations)

In this post we shall discuss about Percentage Calculations. Have a look at the following examples.

• 39 is what percent of 186 ?

• Remember friends. The number that follows 'OF' should always come in the Denominator. And here I am not going to use any mathematical techniques. Just guessing the answer with the given numbers. Remember, No need to get the EXACT answer. Approximate answers will be sufficient (Until you have options like A)12.06 B)12.63 C)12.89 etc....)
• So, here we have to calculate (39/186) X 100 

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Mental Maths (Additions)

In this post, we will show you how to do Additions Mentally. Have a look at the Following Examples........

• 342 + 557 + 629 + 746 + 825 = ?

• When we are adding three-digit numbers, first add-two-digits at a time (Units and Tens Place).
• 42 + 57 + 29 +| 46 + 25 = 199
• To add 42 and 57, mentally treat 57 as 50 + 7 ( Because 50 would facilitate quick addition)
• So, 42 + 57 = (42 + 50) + 7 = 92 + 7 = 99
• Similarly, 99 + 29 = (99 + 20_ + 9 = 128
• 128 + 46 = (128 + 40) + 6 = 174
• 174 + 25 = (174 + 20) + 5 = 199
• The last two digits (the units place and the tens place)

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