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?
2^1/x , 1/x, 1/x², 2^x, 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?
2^1/2, 3^1/3, 4^1/4, 6^1/6, 12^1/12

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!
 

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?
   2^1/x , 1/x, 1/x², 2^x, 1/√-x 
2. Which among the following is the largest?
   2^1/2, 3^1/3, 4^1/4, 6^1/6, 12^1/12
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 :)

For comprehensive CAT Prep, click here.

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.

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.