Showing posts with label MBA. Show all posts
Showing posts with label MBA. Show all posts

## Sunday, June 29, 2014

### Probability Basics : Lesson 1

Today we explore the basic concepts of Probability.

Probability is the measure of the likelihood of an "event" to occur.
For example, when we toss a fair coin, the chances of a head turning up are 1/2. When we roll a dice the chance of 2 appearing is 1/6.

### Important Terms:

1. Sample Space : The collection of all results is called the sample space of the event.
For example, when a coin is tossed, the Sample space(S) is the set {Head, Tails}.
When a dice is rolled, S = {1,2,3,4,5,6}

2. Event: A subset of the S is called an event. For example, when a coin is tossed, {Head}, {Tail} are events. Note that an event set can contain multiple items. For example when 2 coins are tossed, {Head,Head} is considered an event.

3. Equally Probable Events: When 2 events have the same likelihood of occuring, they are known as Equally Probable events. For example the chance of head and tails turning up on the toss of a coin are Equally Probable events.

### Probability

The Probability of an event occurring is defined as the number of cases favorable for the event divided by total number of events in the sample space.

If the event be called as 'A', the probability is represented as P(A)

Example: Probability that head shows up on tossing a coin
P(A) = Favorable Cases/Sample Space = 1/2

P(A') is used to represent the probability of event A not occurring.

Note: P(A) + P(A') = 1

If we have 2 events A,B as the overall sample space, then:

P(A) = A / (A+B) and P(B) = B / (A + B)

### Independent Events and Mutually Exclusive Events

A regular confusion among students is the difference between Independent and Mutually exclusive Events.

Let A, B be 2 events. P(A and B) = P (A ∩ B ) is defined as the probability that both A and B occur together.

For 2 independent events A, B, P(A ∩ B ) = P(A) * P(B)
For Mutually Exclusive events, P(A ∩ B ) = 0

This is best understood with an example.

Consider a fair coin and a fair six-sided die. Let event A be obtaining tails, and event B be rolling a 3. Then we can safely say that events A and B are independent, because the outcome of one does not affect the outcome of the other.

Here, P(A ∩ B ) = 1/2 * 1/6 = 1/12.
Here A and B are Independent Events (Not mutually exclusive).

Consider a fair six-sided dice, where even-numbered faces are colored red, and the odd-numbered faces are colored green. Let event A be rolling a green face, and event B be rolling a 6.

P(A) = 3/6 = 1/2
P(B) = 1/6

But note that A&B cannot occur simultaneously since 6 is always going to turn up on a red face.

Here, P(A ∩ B ) =0
Here A and B are Mutually exclusive events(Not independent).

In our next post we will go deeper into complex probability theory and solve a few problems and provide video solutions for the same.

## Friday, May 30, 2014

### XAT 2014 Solved Question Paper : Video Solutions.

Today we look at a few questions that appeared in XAT 2014 exam. Note that XAT 2014 questions are also a good set of practice questions for CAT 2014.

The questions below have the question followed by a Video Solution!

1.Evaluate the following:
The solution to this problem is explained in the Video below:

2. Two numbers, 297B and 792B, belong to base B number system. If the first number is a factor of the second number then the value of B is

11
12
15
17
19

3. Aditya has a total of 18 red and blue marbles in two bags (each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag, the probability of both being red is 5/16. What is the probability of both marbles being blue?

4. The probability that a randomly chosen positive divisor of 1029 is an integer multiple of 1023 is a2/b2, then 'b - a' would be:

8
15
21
23
45

5. The number of the possible values of X in the equation |X + 7| + |X - 8| = 16 is

0
1
2
3
4

6. A polynomial ax3 + bx2 + cx + d intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:

-2
0
1
2
Cannot be Determined

7. S = ax/(b+c+x) where all parameters are positive. If x is increased and all other terms are kept constant, S will

Increase
Decrease
Increases and then decreases
Decreases and then increases
Cannot be determined

8. x, 17, 3x - y2 - 2, and 3x + y2 - 30, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:

2
3
5
7
11

In our future posts, we will be adding more questions from XAT 2014, which should be also be a very good practice set for CAT 2014.

## Thursday, May 29, 2014

### CAT 2014 : Number Systems - Solutions to Questions that have appeared in Previous CAT Papers.

In our previous blog post, we had picked 3 questions from previous CAT paper. Today we will look at solving these questions. In the process, we will be doing a deeper dive into a couple of important concepts.

Question 1: If x = -0.5, which of the following has the smallest value?
21/x , 1/x, 1/x2, 2x, 1/√-x

Solution: In solving this problem, we will first need to understand a couple of important concepts on Powers of numbers for CAT 2014. The video below explains all the concepts and basics related to it.

Now that we have the concept clear, we can look at the solution to this particular problem.

Question 2: Which among the following is the largest?
21/2, 31/3, 41/4, 61/6, 121/12

Solution: The solution relies on another basic concept of Number systems to compare different numbers with different exponents . The concept and the solution are given below.

Question 3: How may 2 digit numbers increase by 18 when the digits are reversed?

Solution: Note that 2 digit numbers can be expressed as ab, where a,b are digits. So the original number is 10a + b, reversed number 10b + a.

The complete solution along with a few more basics for CAT 2014 can be viewed below.

We will be returning with our next post in a couple of days time! Happy Learning!

## Sunday, May 25, 2014

### CAT 2014 : Number Systems - Questions that have appeared in Previous CAT Papers.

In Today's post, we try to look at 3 problems that have appeared in past CAT papers, and provide clues to solve them.

The complete solution will be available in our next post.

1. If x = -0.5, which of the following has the smallest value?
21/x , 1/x, 1/x2, 2x, 1/√-x
2. Which among the following is the largest?
21/2, 31/3, 41/4, 61/6, 121/12
3.  How many 2 digit numbers increase by 18 when the digits are reversed?

Hints:
1. A positive number raised to any real number will always be positive. For eg, 4-1/10 will be greater than 0.
2.  Convert all numbers to have the same exponent. Then compare the numbers.
3. Let the number have digits a,b. Original number is 10a+b, reversed is 10b+a. Take the difference and try to solve it :)

## Saturday, May 24, 2014

### Solved Examples : Number Systems for CAT and other MBA Exams.

In the previous post, we asked a few questions to help us understand the various concepts in number systems by examples.

Here are Video Solutions to all these problems :).

1. What happens when you multiply 3 even numbers? 2 even numbers and an odd number? 2 odd numbers and an even number? and 3 odd numbers?
2. What happens when you multiply 'N' even numbers? and 'N' odd numbers
3. Can product of 4 consecutive numbers be Odd?
The solution to all these 3 problems are explained in the video below.

We then asked the question:  Whats the smallest number should be added to 156789 to make it divisible by 11?

To solve this problem, we need to understand divisibility tests by 11. This and the solution to the problem is explained in the video below.

Our Next question was: Whats the smallest number that should be added to 677 to make it divisible by 4, 5, and 11?

To solve this, its important to understand concepts of LCM. The question is solved with concepts below.

Our Next question was related to power cycles: What is the units digit of 72999?
Detailed solution with basic power cycles concept is below.

Our Last question was in advanced Power cycle: What will be the last 2 digits when 25625 is multiplied by 375?

Concept explanation with detailed solution is given below.

Do let us know what you think about these solutions.
We will be back with more a more detailed Number Systems Lesson in the next week.

In other news: TCS will be the official test partner for CAT the next 5 years. This was announced a few days back.

## Friday, May 16, 2014

### Number Systems for CAT and Other MBA Exams.

Number systems is an important topic for CAT and all other MBA Exams. The various topics under Number systems include :

1. Classification of Numbers : Natural numbers, Whole numbers, Fractions, Real Numbers, Complex  numbers etc.
2. Rules on Number Operations : For eg, sum of 2 odd numbers is even etc.
3. Divisibility Rules.
4. Properties of Prime and Composite numbers, factorisation.
5. Power Cycle of Numbers

Today we will start by asking questions for you to ponder over, and answer each of them in the next set of blog posts with detailed video concepts.
1. What happens when you multiply 3 even numbers? 2 even numbers and an odd number? 2 odd numbers and an even number? and 3 odd numbers?
2. What happens when you multiply 'N' even numbers? and 'N' odd numbers
3. Can product of 4 consecutive numbers be Odd?
4. Whats the smallest number should be added to 156789 to make it divisible by 11?
5. Whats the smallest number that should be added to 677 to make it divisible by 4, 5, and 11?
6. What is the units digit of 72999
7. What will be the last 2 digits when 25625 is multiplied by 375?
Through these problems, we hope to cover the complete Number systems concepts, and help you prepare better for CAT and other leading MBA Exams.

## Thursday, May 15, 2014

### CAT 2014: Getting Started

With less than 6 months to go for CAT, Oliveboard will be starting its concept blog today.

What to Expect:

1. Each topic with basic concepts.
2. Worked out examples for these topics.
3. Exercises
4. Video solutions to selected questions.

We are sure this will help you ace CAT 2014 and other MBA exams!

Register at Oliveboard for more.

Have a doubt? Leave a comment and we will get back to you at the earliest. Or you can email us at : support [at] oliveboard [dot] in