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Hello Everyone ...This section is very dry ...Time to start something new ...

So, i have thought of this new initiative to make a repository of all formulae / concepts and fundas one would require to make a successful attempt at GMAT ...

So, over a period of time, GMAT aspirant can find concepts pertaining to all topics under one thread ...

So, everybody start contributing ...any short cut or self discovered ways to tackle different kinds of problems are also most welcome ..
I shall contribute as and when time permits.

I shall begin by posting simple formulae initially and then gradually we can move towards tougher concepts as well !!

P.S : avoid posting questions in this thread , you may post a specific problem to support your concept, otherwise let us dedicate this thread purely for fundas !!

Shall post soon ...

Stay glued ...

Let us begin !!

I'll start with simple geometry first ( triangles to be specific) , quadrilaterals, solid geometry and co-ordinate geometry will be followed soon

For n sided quadrilateral, sum of angles = 180 (n-2)
Regular polygon is a polygon which has all equal sides and equal angles
Each angle of regular polygon = 180 (n-2) / n
Remember, for regular pentagon, each angle is 108 degrees
And, for regular hexagon, each angle is 120 degrees.

Area of Triangle = ˝*_base_*height
= ˝ *product of any 2 sides *sine of included angle
= root (s(s-a)(s-b)(s-c)) where s=semi perimeter = (a+b+c) /2
…and many more (not really required on GMAT)

Area of equilateral triangle = (root 3) / 4 * side^2
For a given perimeter of a triangle, area is maximum when sides are equal i.e equilateral triangle has max area .

Ratios of sides in a 30-60-90 degree triangle is 1 : root 3 : 2
i.e side opposite to 30 degrees is ˝ times hypotenuse
and side opposite to 60 degrees is (root3)/2 times hypotenuse

Ratios of sides in a 45-45-90 triangle is 1:1:root2
i.e hypotenuse = side *root 2

Side opposite to the largest angle is the largest side.
Any side of a triangle is lesser than the sum of other 2 sides and greater than the difference of other 2 sides.

To get area of triangle in a DS question we need either of the following things :
1)All 3 sides
OR 2) 2 sides and an angle
OR 3) 1 side and 2 angles
Remember, just 3 angles are not sufficient to calculate area since we can construct infinite triangles from given 3 angles.

To find whether triangle is acute, abtuse or right angled triangle :
If a,b,c are 3 sides of the triangle such that c is the largest side, then :
If c^2 is greater than a^2 + b^2 …..obtuse angle
If c^2 = a^2 + b^2 …right angled triangle
If c^2 is lesser than a^2 + b^2 …..acute angled triangle
i.e compare the squares of the largest side wrt sum of squares of other 2 sides !!

All congruent triangles are similar, but all similar triangles are not congruent
For similar triangles, ratios of areas of triangles is equal to square of ratios of sides.

Stay Glued !!

concepts regarding slope today :

slant of the line can be understood by its slope...
we know, slope = m = tan @ = (y2-y1)/(x2-x1)...
Let @ be the inclination of line in degrees wrt. Positive X- Axis...

Then :
1) When @ is acute, slope is positive
2) and when @ is obtuse, slope is negative...( or acute inclination of line wrt to negative X-Axis )
3) when line is parallel to X - Axis slope is zero
4) When line is parallel to Y-Axis slope is not defined..

To put things in perspective, slope is dependent on inlination @ wrt to +ve X-Axis .

When @ is between 0 and 45 : m is between 0 and 1
When, @=45, m= 1
When @ is between 45 and 90 : m is between 1 and infinity
When @ = 90 ; slope = not defined
When @ is between 90 and 135 : m is between infinity and -1.
When @ = 135 ( or 45 degrees wrt to -ve X-Axis ) ; m= -1
When @ is between 135 and 180 : m is between -1 and 0.

This takes care of entire range of angles from 0 to 180 and its corresponding slope...

Slopes and quadrants :

Line with a positive slope intersects atleast 1st and 3rd quadrant, and line with a negative slope intersects atleast 2nd and 4th quadrant...

Position of a line in a particular quadrant not only depend upon the slope, but also its intersecting pts on X & Y Axis..or simply the intercepts..

so, a negative slope does not necessarily mean line passes thru fourth quadrant..
all parallel lines have same slope...so there are infinite line with same slope..and these lines could pass thru any of the 4 quadrants..
but given a slope and one of its intercepts, line becomes fixed..

For perpendicular lines, product of slopes is -1 i.e slope of a perpendicular line is -ve reciprocal of the other ..

Hope this helps !!

Cheers !!

What is the units digit of 3 raise to 801?


Find Patterns and it shows up pretty quickly:

3^1= 3
3^2= 9
3^3= 27
3^4= 81
3^5= 243
3^6= 729

Every 4 powers and you get the same number as the units digit. We know 800 is a multiple of 4. And 801 is therefore one greater than a multiple of 4. So the units digit is 3, as above when the exponent is 1 greater than a multiple of 4.

If you have an ODD (not even) number of numbers in your set, the sum will always be a multiple of the number of numbers.

5 numbers in this set of consecutive numbers:
1 + 2 + 3 + 4 + 5 = 15.
YES, 15 is a multiple of 5.

6 numbers in a set of consecutive numbers:
11 + 12 + 13 + 14 + 15 + 16 = 81.
NO, and there are 6 numbers (an EVEN number of numbers). 81 isn't a multiple of 6.

If you multiply an ODD number of numbers in a consecutive number set, it WILL ALWAYS be divisible by the number of numbers because a group of 5 consecutive numbers MUST include a multiple of 5 in it. (2, 3, 4, 5, 6) or (18, 19, 20, 21, 22).

For example, a series of 5 consecutive integers, it WILL ALWAYS be divisible by 5.

2 × 3 × 4 × 5 × 6 = 720

Try this example:
6 numbers in a row. Here we added a 1 in the front.

1 × 2 × 3 × 4 × 5 × 6 = 720

Here there are 6 numbers, and yes, 720 is divisible by 6.