GMAT/CAT PREPARATION EMAIL COURSE DAY 22

Supplementary Angles:
If the sum of two angles is 180 degrees ie, if they form a straight line , the two angles are supplementary.
Each angle is called the supplement of each other.

Complementary Angles:
If the sum of two angles is 90 degrees.

Reflex Angles:
Angles larger than two right angles but less than a full circle (between 180° and 360°) are called reflex angles.

Acute Angles:
Those angles whose measure is less than 90 degrees

Obtuse Angles:
Those angles whose measure is greater than 90 degrees but less than 180 degrees.

Right Angles:
If two supplementary angles are equal, they are both right angles.
A right angle is half of a straight line and measures exactly 90 degrees.




Intersecting Lines:

When two lines intersect, four angles are formed.
Adjacent angles are supplementary and vertical angles are equal.





Vertical Angles:

Two angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles. These angles are equal in measure.

Straight Angles:

Has its sides lying along a straight line and equal to 180 degrees.

Adjacent Angles:

Angles that share a common vertex and edge but do not share any interior points are called adjacent angles.

Parallel Lines and Transversals:

A transversal (line t) across parallel lines form four equal acute angles and four equal obtuse angles.

The top line (line l) is parallel to the bottom line (line m) and line t is the transversal.




Angles 1, 2, 5 and 8 are all equal and acute.
Angles 3, 4, 6 and 7 are all equal and obtuse.

In addition, each of the acute angles is supplementary to each of the obtuse angles. Angles 1 and 4 are supplementary, as are 2 and 3, 2 and 6, and so on.

GMAT/CAT PREPARATION EMAIL COURSE DAY 21

COORDINATE GEOMETRY

Point on a Plane:

Point of Origin is (0,0)

Points in the xy-plane are represented by two numbers called coordinates:

The first number in the pair is the x-coordinate, which is is the horizontal distance of the point from the origin.Points with positive x-coordinates are on the right of the y-axis and Points with negative x-coordinates are on the left of the y-axis.

The second number is the y-coordinate, which is the vertical distance from the origin.Points with positive y- coordinates are above the x-axis. Points with negative y-coordinates are below the x-axis.

A point is represented by (x, y) where x is called the abscissa and y is called the ordinate.


Distance Between Two Points:

To find the distance between points on a graph by using the distance formula:
2 2
Distance = sqrt((x1 -x2) + (y1 - y2) )


Finding the Slope:

Slope = Change in y/Change in x
= Vertical Rise/Horizontal Run

The slope of the line that contains the points A (2, 3) and B (0, -1) is:

(y2 - y1) / (x2 - x1) = (-1 - 3) / (0 - 2) = -4 / -2 = 2

Slope-Intercept Equation:

Equation to Find the Slope:

To find the slope of a line from an equation, put the equation into the slope-intercept form:
y = mx + b

The slope is m and the y-intercept is b.

To find the slope of the equation 4x + 3y = 4, rearrange it:

4x + 3y = 4
3y = -4x + 4
y = -4/3 x + 4/3

The slope is -4/3


Finding an Intercept:

To find the y-intercept, either:

a)Put the equation into y = mx + b (slope-intercept) form and b is the y-intercept

b)Replace x = 0 into the equation and solve for y.

To find the x-intercept, Replace y = 0 into the equation and solve for x.

GMAT/CAT PREPARATION EMAIL COURSE DAY 20

AVERAGE, MEDIAN AND MODE

Average or Arithmetic Mean

To find the average of a set of numbers, find the sum and divide by the number of numbers.

Average = Sum of the terms/Number of terms

To find the average of the five numbers 12, 15, 23, 40, and 50, first add them:
12 + 15 + 23 + 40 + 50 = 140.

Then divide the sum by 5: 140 / 5 = 28.


If Average is known to Find the Sum:

Sum = (Average) X (Number of terms)

If the average of ten numbers is 70, then their sum is 10 X 70, or 700.

To Find a Missing Number:

To find a missing number when the average is given , use the sum.

If the average of four numbers is 8, then the sum of those four numbers is 4 X 8, or 32.
Suppose three of the numbers are 4, 7, and 8.

These three numbers add up to 19 .
Which leaves 13 for the fourth number.


Median:

The median of a set of numbers is the value that falls in the middle of the set.

If you have five test scores, and they are 88, 85, 59, 94, and 73, you must first list the scores in increasing or decreasing order: 59,73, 85, 88, 94.The median is the middle number, or 85.

If there is an even number of values in a set (six test scores, for instance), simply take the average of the two middle numbers.


Mode:

The mode of a set of numbers is the value that appears most often.

If your test scores were 89, 56, 68, 88,99, 95, 95, 84, and 95, the mode of the scores would be 95 because it appears more often than any other score.

If there are two most common value in a set, the set has more than one mode.


Standard Deviation

The standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance.

Standard deviation is a widely used measure of the variability or dispersion. It may be thought of as the average difference of the scores from the mean of distribution, how far they are away from the mean.

A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

GMAT/CAT PREPARATION EMAIL COURSE DAY 19

Group Discussions are common in selection process .People watching your discussion see at your body language, the way you speak, the way you show your presence at the GD, the way you move with other people etc.Here are some of the important do's and dont's in GD


DO's:

Do Have confidence in yourself.

Do think of your GD mates as your friends.

Do get updated with current affairs and general topics.

Do take a pen and paper with you.

Start the discussion if possible because The person who speaks first and last will get additional points.

Do start with greetings if you are the first to speak.

Do Introduce yourself.Just saying your name will be sufficient.

Do speak with optimum volume level that will be sufficient for the other members to hear you.

Do Validate your points with stats. Give proofs/incidents to make your point more effective.

The content of your speech matters.

Do make note of important points that you have in mind and what others say.

Do Look at all the people. Move your heads/eyes towards all the people.

Try to use words like "As my friend said", "As my friend rightly pointed out", "I agree with what he/she said" etc. If you know his/her name, use his/her name.

If the discussion gets centered at the same point, try to bring in new dimension to the discussion with your points.

Keep your points short and simple.

Try to conclude the discussion. During conclusion, list out all the important points that were discussed from you notes.

DONT's:

If you are sure about your points start the discussion else listen to what others so that you can get some idea on the topic.

Don't speak irrelevant to the topic. If the discussion drifts away from the topic, pull it back.

Don't sit quiet for a long time or till all the people finish speaking. Grab your chance as soon as possible.

Don't point on to others with your finger.

Don't speak too loud or too low voice.

Don't leave a pause between two points.

Don't jump from one point to another abruptly.

Don't use negatives like "I don't agree with you", I strongly object" etc instead Use words like "My points differs from your point" .

Don't shake your legs.

Don't cross your fingers.

Keep yourself cool throughout the discussion and be the winner.

GMAT/CAT PREPARATION EMAIL COURSE DAY 18

CALENDAR PROBLEMS
For solving the calendar problems we may need the following info.

We can find the number day on which a particular date falls by finding the number of odd days.

Odd days are obtained by finding the remainder when the no of days are divided by 7

The no of days in each month in a year is Jan-31, Feb-28(29), Mar-31, Apr-30, May-31, Jun-30, Jul-31, Aug-31, Sep-30, Oct-31, Nov-30, Dec-31

No of odd days in each month in a year -Jan-3, Feb-0(1), Mar-3, Apr-2, May-3, Jun-2, Jul-3, Aug-3, Sep-2, Oct-3, Nov-2, Dec-3

Leap year: A year is said to be Leap year if it contains366 days (ie,29 days in February)
How to find whether a year is leap year or not ?
1) We get a leap year if that year is divisible by 4 exactly
2) Years divisible by 100 and not by 400 is not a leap year

1st January 0001 was a Monday.

Calendar repeats after every 400 years.

Calendar moves ahead by number of odd days.

In a normal year 1st January and 2nd July and 1st October fall on the same day.

In a leap year 1st January 1st July and 30th September fall on the same day.

Ordinary year = 52 weeks + 1 odd day

Leap year = 52 weeks + 2 odd day

100 Years = 76 ordinary years +24 leap years
100 years has 5 odd days
400 years has (20+1) odd days ie , 0 odd days.

Here are the steps to find out the number of odd days.
Step 1: Find leap year or not.
Step 2: Find out total odd days on months.
Step 3: Find out the total odd days on year.
Step 4: Finally add the total number of odd days between the given dates.

Jan 1, 2001 is a Monday, depending on odd day, we have
1 is Monday
2 is Tuesday
3 is Wednesday
4 is Thursday
5 is Friday
6 is Saturday
0 or 7 is Sunday

GMAT/CAT PREPARATION EMAIL COURSE DAY 17

CLOCKS:

Clock angle problems relate two different measurements - angles and time.
To answer the problem the relationship between the time and the angle between the hands .

-->A dial of the clock is divided into 60 parts each called minute spaces.
-->The hour hand goes 5 minute spaces in one hour and minutes hand goes 60 minute spaces in one hour.
-->Thus the minute hand covers 6 degress per minute.
-->The hour hand covers 30 degrees per hour.
-->The minute hand gains 55 minute spaces over the hour hand in one hour
-->When two hands are in 90 degree they are 15 minute spaces apart. This occurs twice in an hour.
-->When the two hands are in opposite directions(ie,180 degrees)they are 30 minute hands apart this occurs once in an hour
-->Two hands are in straight line when they coincide or are in opposite directions
-->The angle between the two hands = 6(x-11/12m)
X= hour hand convert into minute spaces i.e.* 5 of the earlier clock
M = the later part of the time i.e. minutes

GMAT/CAT PREPARATION EMAIL COURSE DAY 16

Here are some of the tips which you can use to calculate faster

http://catdumps.blogspot.com/2009/05/speed-conversions.html

http://catdumps.blogspot.com/2009/05/temparature-conversions.html

http://catdumps.blogspot.com/2009/05/adding-time.html

http://catdumps.blogspot.com/2009/05/converting-kilometres-to-miles.html

http://catdumps.blogspot.com/2009/05/converting-kilos-to-pounds.html

WINDOWS KEYBOARD SHORTCUTS

Below is a listing of Windows keys that can be used on computers running a Microsoft Windows operating system and using a keyboard with a Windows key. In the below list of shortcuts the windows key is represented by "WINKEY". Shortcut Keys Description WINKEY + D Minimizes all windows and returns the user to the desktop.WINKEY + M Minimizes...
Read more....

GMAT/CAT PREPARATION EMAIL COURSE DAY 15

WORK RELATED PROBLEMS

Generally if a person can do the work in 'N' days means (1/N) is the work done by the person in one day.

This can be called as work rate of the person.

Work rate of Person = 1/T

where T is the numbers of days/time required to complete the given work by the given person.

The other case is if a person's one day work(Work rate) is know then the reciprocal would give the total number of days required to complete the work.

Time required = 1/one day work (work rate)

and another thing you should know if how much time will group of people take to complete the work if their individual work rates are known,this formula could be useful.

1/Ta+1/Tb+...+1/Tn=1/Tco

Where Ta,Tb,...Tn are individual time taken and Tco is combined timetaken

Note:
If A is twice good as B means
work rate of A to B is 2:1
Time taken by A and B to complete the work is 1:2

GMAT/CAT PREPARATION EMAIL COURSE DAY 14

SPEED AND DISTANCE RELATED PROBLEMS:

We define speed as distance travelled in a particular time,

Speed = distance /time

but once we have the equation, we can use any of its variations,

Time = Distance/speed

Distance = speed*time

CONVERSION:

1km/hr=1000m/h=1000/3600m/sec=5/18m/sec

1 m/s = 18/5 Km/hr

1 km/hr =5/8 miles/hr

1 mile/hr = 22/15 feet/sec

average speed = total distance/total time taken