Problem Solving

Hello,

Q. Rectangular Floors X and Y have equal area. If floor X is 12 feet by 18 feet and Floor Y is 9 feet wide, What is the length of Floor Y, in feet?

Options:
A. 13.5 B. 18 C. 18.75 D. 21 E. 24
(you guys are thinking, what a 'F' problem )
Let's check my method. we will solve it with options.

Ans. Area of Floor X = Area of Floor Y
means Length*Width of X = Length*Width of Y

See carefully, Area of Floor X is Integer and 6 is the unit digit. Am i right? 

Option A and C eliminated because Answer will be in decimals. Remain with B,D and E

Option B has unit digit of 2 and Option D has unit digit of 9 So These are also eliminated.

So Option E is the answer. Now you can check it with your method. 
(12*18 = 9*24)






Er. Ankur Garg

Problem Solving

Hello frndz,

Happy Diwali to all!!!!!!! Today we will do couple of problem solving...

Q. A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4580. By how much was the project over its budget?

Ans. (Short Method )

We know the actual amount spent during four month i.e. $4580. So we need to calculate budget amount for the same period.
Budget amount per month = 12600/12 = $1050
So, budget amount for four months = 1050*4 = $4200

(We have a budget of $4200 for these four months and have spent $4580. Ofcourse, It's a Indian situation)

Amount over budget = 4580 - 4200 = $380
This is the answer.........

Q. If the sum of 5,8,12,15 is equal to the sum of 3,4,x and x+3, what is the value of x?

Ans. (Simply addition method...)

Given,

5+8+12+15 = 3+4+x+x+3

40 = 2x+10

30 = 2x

x = 15....... Solved!!!!!!!

Q. For which of the following values of n is (100+n)/n NOT an integer?

Options are: A. 1 B. 2 C. 3 D. 4 E. 5

Ans. (Do this with the help of option; prefer to select C first...)

Put 3 in place of n, we get;

103/3 = NOT Integer

So C is the answer...............

Okie guys....Bye will catch u later!!!!!!!1

Er. Ankur Garg

www.nascentedutech.com

Day 13: Simplifying Algebraic Expressions

Hello frndz,

Today we will start with Algebra... First know about introduction of Algebra.


:- Algebra is based on a set of combination of variable and operations performed on that.
For eg. x+5 is an algebraic expression.

:- In expression 19x^2 - 6x + 3; 19 is the coefficient of x^2, -6 is the coefficient of x and 3 is a constant term.


:- When working with algebraic expressions, it is necessary to simply them by factoring or combining like terms.
For eg. 6x + 5x = (6 + 5)x = 11x


:- Simply (3xy - 9y) / (x - 3)
3y(x - 3) / (x - 3) = 3y


:- To multiply two algebraic expressions, each term of one expression is multiplied by each term of the other expression.
For eg. (3x - 4)(9y + x)
3x (9y + x) - 4 (9y + x) = 3x * 9y + 3x * x - 4 * 9y - 4 * x
= 27xy + 3x^2 - 36y - 4x


The given expression can be evaluated by substituting values of variables in the expression.
For eg. If x=3 and y=-2
then above expression can be evaluated as
27(3)(-2) + 3(3)^2 - 36(-2) - 4(3)
= -162 + 27 + 72 - 12
= -75


Okie guys, Keep practice on!!!



Er. Ankur Garg
garg.ankur6@gmail.com

Day 12: Discrete Probability

hello frndz,

Today we will learn about Discrete Probability!!

:- Discrete probability is an experiments that have a finite number of outcomes.
For eg. Rolling a device numbered 1 to 6 has 6 possible to outcomes: 1,2,3,4,5,6


:- D.P of an event is an experiment that has number of outcomes for event E out of all possible outcomes.
For eg. Rolling a device with getting odd number on face. Here Odd number on face is an event E.
Number of outcomes for event E = {1,3,5} = 3
Total possible outcomes = 6
Discrete probability = 3/6 = 1/2

(general Formula: P(E) = The number of outcomes in E / The total number of possible outcomes)


:- P(E) is a number between 0 and 1. If P(E) = 0, Event E is not possible and If P(E) = 1, then Event E is certain.

For eg. Probability of getting an odd number divisible by 2 is 0. (Not possible)
Another; probability of getting an even number divisible by 2 is 1. (Always)


:- "Not E" is the set of outcomes that are not outcomes in E.
For eg. In previous eg. of rolling device, getting even number on face = 1 - getting odd number of face


:- "E or F" is the set of outcomes in E or F or both.
"E and F" is the set of outcomes in both E and F.

For eg. In previous example of rolling device, getting an odd number(E) or prime number(F),
P(E or F) = P(E) + P(F) - P(E and F)
P(E and F) = {3,5}/6 = 2/6 = 1/3
P(E) = 1/2; P(F) = {1,3,5}/6 = 3/6 = 1/2

So P(E or F)  = 1/2 + 1/2 - 1/3 = 2/3



:- If E and F are independent events and occurrence of either event does not affect the probability that the other event occurs, then P(E and F) = P(E)P(F)
For eg. Rolling a device with getting even number(E) and Rolling another device with {5,6}(F) are independent events.
P(E) = 1/2
P(F) = {5,6}/6 = 1/2
So P(E and F) = 1/2*1/2  = 1/4
In this Case, P(E or F) = P(E) + P(F) - P(E)P(F)


:- If E and F are mutually exclusive events and "E and F" is not possible, then P(E and F) = 0
For eg. Rolling a device and flipping a coin are mutually exclusive events.
In this Case, P(E or F) = P(E) + P(F)



Okie guys, Keep practice On!! This is the end of Arithmetic.. From tomorrow on wards, we will go for Algebra..


Er. Ankur Garg
garg.ankur6@gmail.com

Day 11: Counting Methods

Hello frndz,

Today we will learn about Counting Methods..


:- If an object is to be chosen from a set of m objects and a second object is to be chosen from a different set of n objects, then there are mn ways of choosing both objects simultaneously.

For eg. Suppose the objects are items on a menu. If a meal consists of one entree and one dessert and there are 5 entrees and 3 desserts on the menu, So in how many different ways one can be ordered from the menu?

Solution: Lets take entrees are ABCDE and desserts are XYZ.
then ways are AX, AY, AZ, BX, BY, BZ, CX, CY, CZ, DX, DY, DZ, EX, EY and EZ.
total number of different ways : 15
(General Formula: total number of first objects * total number of second objects
i.e. 5*3 = 15)



:- A symbol that is often used with the multiplication principal is the factorial. It is defined as the product of all the integers from 1 to n i.e. n!
For eg. 2! = 2*1 ; 3! = 3*2*1 etc...
(Note: 0! =1! = 1)



:- A permutation is a selection process in which objects are selected one by one in a certain order (Order matters).
For eg. If k objects to be selected from a larger set of  n objects, permutation is
(n,k) = n! / (n-k)!


:- A combination is a selection process in which objects are selected without regards to order.
For eg. If k objects to be selected from a larger set of  n objects, combination is
(n,k) = n! / k!(n-k)!

:- (n,k) = (n,n-k)

For eg. (5,2) = 10 = (5,3)

Okie guys, Keep practice on !!!

Er. Ankur Garg

garg.ankur6@gmail.com

Day 10: Sets

Hello frndz,

Today we will learn about Sets!!!!


:- A set is a collection of numbers or objects. The objects are called the element of the set.
For eg. Set S = {1,2,5} or {Car, Bus, Bicycle}


:- If set S have a finite number of elements, then the numbers of elements is denoted by |S|.
In above example, |S| = 3


:- If all the elements of a set S are also elements of a set T (or having extra), then S is a subset of T.
For eg. S = {1,2,5} is a subset of T = {0,1,2,3,5}


:- For any two sets A and B, the union of A and B is the set of elements that are in A or in B or in both.
For eg. If A = {3,4}, B = {4,5,6}
then A U B = {3,4,5,6}
(Note: Common values will be considered only once).


:- For any two sets A and B, the intersection of A and B is the set of elements that are both in A and in B.
In above example, Intersection (A,B) = {4}


:- General Formula: Union (A,B) = |A| + |B| - Intersection (A,B)


:- Venn Diagram:

Elements of First circle: A + C
Elements of Second circle: B + C
Intersection of both circle: C only

Okie guys, Keep practice on!!! Er. Ankur Garg garg.ankur6@gmail.com

Day 9: Descriptive Statistics

Hello frndz,

today we will learn about Descriptive Statistics..

:- Average: The average of n number is defined as the sum of the n numbers divided by n.
For eg. the average of 6,4,7,10 and 4 is (6+4+7+10+4)/5 = 31/5 = 6.2


;- Median: To calculate the median of n numbers, first order the numbers from least to greatest; if n is odd, the median is the middle number.

For eg. the median of 6,4,7,10,4

step 1: first order it form least to greatest - 4,4,6,7,10
step 2: find the middle number i.e. 6

So median is 6

whereas, if n is even, the median is the average of the two middle numbers.
For eg. the median of 4,6,6,8,9,12 = (6+8)/2 = 7

(Note: if n is odd, median is (n+1)/2; else the average of n/2 and n/2 + 1)



:- It is not always true that half of the data in a series is less than median and half of the data is more than the median.
For eg. 3,5,7,7,7,7,7,7,8,9,9,9,9,10,10
Here the median is 7, but only 2/15 of the data is less than the median.



:- Mode; The mode of a list of numbers is the number that occurs most frequently in the list.
For eg. mode of 1,3,6,4,3,5 is 3 (occurs twice)

(Note: A list of numbers may have more than one mode.)


:- Range: Range is defined as the greatest value minus the least value.
For eg. the range of 11,10,5,13,21 is
21-5 = 16


:- Standard deviation: To calculate standard deviation;

step 1: find the arithmetic mean (average)
step 2: find the difference between the mean and each of the n numbers
step 3: square each of the differences
step 4: find the average of the squared differences
step 5: take the non negative square root of this average

For eg. standard deviation of 0,7,8,10,10

step 1: average = 7
step 2: differences = -7,0,1,3,3
step 3: square of differences = 49,0,1,9,9
step 4: average of step 3 = 68/5 = 13.6
step 5: square root of step 4 = 3.7

So S.D = 3.7

(Note: the more data are spread away from the mean, the greater the standard deviation and same as vice-versa).




Okie guys, keep practice on!! catch u soon.....


Er. Ankur Garg
garg.ankur6@gmail.com